Volume
LIPIcs, Volume 261
50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Event
ICALP 2023, July 10-14, 2023, Paderborn, GermanyEditors
Publication Details
- published at: 2023-07-05
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-278-5
- DBLP: db/conf/icalp/icalp2023
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Document
Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volume
Abstract
LIPIcs, Volume 261, ICALP 2023, Complete Volume
Cite as
50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 1-2486, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@Proceedings{etessami_et_al:LIPIcs.ICALP.2023,
title = {{LIPIcs, Volume 261, ICALP 2023, Complete Volume}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {1--2486},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023},
URN = {urn:nbn:de:0030-drops-180517},
doi = {10.4230/LIPIcs.ICALP.2023},
annote = {Keywords: LIPIcs, Volume 261, ICALP 2023, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 0:i-0:xxxviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{etessami_et_al:LIPIcs.ICALP.2023.0,
author = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {0:i--0:xxxviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.0},
URN = {urn:nbn:de:0030-drops-180523},
doi = {10.4230/LIPIcs.ICALP.2023.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk)
Abstract
We describe recent joint work with Nathan Klein and Shayan Oveis Gharan showing that for any metric TSP instance, the max entropy algorithm studied by [Anna R. Karlin et al., 2021] returns a solution of expected cost at most 3/2-ε times the cost of the optimal solution to the subtour elimination LP and hence is a 3/2-ε approximation for the metric TSP problem. The research discussed comes from [Anna R. Karlin et al., 2021], [Anna R. Karlin et al., 2022] and [Anna R. Karlin et al., 2022].
Cite as
Anna R. Karlin. A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{karlin:LIPIcs.ICALP.2023.1,
author = {Karlin, Anna R.},
title = {{A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {1:1--1:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.1},
URN = {urn:nbn:de:0030-drops-180531},
doi = {10.4230/LIPIcs.ICALP.2023.1},
annote = {Keywords: Traveling Salesperson Problem, approximation algorithm}
}
Document
Invited Talk
An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk)
Abstract
In this talk, I will explain a new algorithm for computing exact maximum and minimum-cost flows in almost-linear time, settling the time complexity of these basic graph problems up to subpolynomial factors.
Our algorithm uses a novel interior point method that builds the optimal flow as a sequence of approximate minimum-ratio cycles, each of which is computed and processed very efficiently using a new dynamic data structure.
By well-known reductions, our result implies almost-linear time algorithms for several problems including bipartite matching, optimal transport, and undirected vertex connectivity. Our framework also extends to minimizing general edge-separable convex functions to high accuracy, yielding the first almost-linear time algorithms for many other problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and isotonic regression.
This talk is based on joint work with Li Chen, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva [Chen et al., 2022]. Our result appeared in FOCS'22 and won the FOCS best paper award.
Cite as
Rasmus Kyng. An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kyng:LIPIcs.ICALP.2023.2,
author = {Kyng, Rasmus},
title = {{An Almost-Linear Time Algorithm for Maximum Flow and More}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.2},
URN = {urn:nbn:de:0030-drops-180543},
doi = {10.4230/LIPIcs.ICALP.2023.2},
annote = {Keywords: Maximum flow, Minimum cost flow, Data structures, Interior point methods, Convex optimization}
}
Document
Invited Talk
Context-Bounded Analysis of Concurrent Programs (Invited Talk)
Abstract
Context-bounded analysis of concurrent programs is a technique to compute a sequence of under-approximations of all behaviors of the program. For a fixed bound k, a context bounded analysis considers only those runs in which a single process is interrupted at most k times. As k grows, we capture more and more behaviors of the program. Practically, context-bounding has been very effective as a bug-finding tool: many bugs can be found even with small bounds. Theoretically, context-bounded analysis is decidable for a large number of programming models for which verification problems are undecidable. In this paper, we survey some recent work in context-bounded analysis of multithreaded programs.
In particular, we show a general decidability result. We study context-bounded reachability in a language-theoretic setup. We fix a class of languages (satisfying some mild conditions) from which each thread is chosen. We show context-bounded safety and termination verification problems are decidable iff emptiness is decidable for the underlying class of languages and context-bounded boundedness is decidable iff finiteness is decidable for the underlying class.
Cite as
Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Context-Bounded Analysis of Concurrent Programs (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.3,
author = {Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg},
title = {{Context-Bounded Analysis of Concurrent Programs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {3:1--3:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.3},
URN = {urn:nbn:de:0030-drops-180559},
doi = {10.4230/LIPIcs.ICALP.2023.3},
annote = {Keywords: Context-bounded analysis, Multi-threaded programs, Decidability}
}
Document
Invited Talk
Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions (Invited Talk)
Abstract
The study of multiprover interactive proof systems, of locally testable codes, and of property testing are deeply linked, conceptually if not formally, through their role in the proof of the PCP theorem in complexity theory. Recently there has been substantial progress on an analogous research programme in quantum complexity theory. Two years ago we characterized the power of multiprover interactive proof systems with provers sharing entanglement, showing that MIP^* = RE [Ji et al., 2020], a hugely surprising increase in power from the classical result MIP = NEXP of [Babai et al., 1991]. The following year Panteleev and Kalachev gave the first construction of quantum low-density parity-check codes (QLDPC) [Panteleev and Kalachev, 2022], thus marking a major step towards the possible realization of good quantum locally testable codes - the classical analogue of which was only constructed quite recently [Dinur et al., 2022]. And finally, less than a year ago Anshu, Breuckmann and Nirkhe used facts evidenced in the construction of good decoders for the new QLDPC codes to resolve the NLTS conjecture [Anshu et al., 2022], widely viewed as a crucial step on the way to a possible quantum PCP theorem.
In the talk I will survey these results, making an effort to motivate and present them to the non-expert. I will explain the connections between them and point to where, in my opinion, our understanding is currently lacking. Along the way I will highlight a number of open problems whose resolution could lead to further progress on one of the most important research programmes in quantum complexity theory.
Cite as
Thomas Vidick. Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{vidick:LIPIcs.ICALP.2023.4,
author = {Vidick, Thomas},
title = {{Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {4:1--4:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.4},
URN = {urn:nbn:de:0030-drops-180569},
doi = {10.4230/LIPIcs.ICALP.2023.4},
annote = {Keywords: quantum interactive proofs, quantum codes}
}
Document
Invited Talk
The Skolem Landscape (Invited Talk)
Abstract
The Skolem Problem asks to determine whether a given integer linear recurrence sequence (LRS) has a zero term. This decision problem arises within a number of different topics in computer science, including loop termination, weighted automata, formal power series, and probabilistic model checking, among many other examples. Decidability of the problem is notoriously open, despite having been the subject of sustained interest over several decades [Halava et al., 2005]. More specifically, the problem is known to be decidable for recurrences of order at most 4 - a result obtained some 40 years ago [Mignotte et al., 1984; Vereshchagin, 1985] - while decidability is open already for recurrences of order 5.
In this talk we take a wide-ranging view of the Skolem Problem. We survey its history and context, starting with the theorem of Skolem-Mahler-Lech characterising the set of zeros of a LRS over fields of characteristic zero. Here we explain the non-effective nature of the existing proofs of the theorem. Among modern developments, we overview versions of the Skolem-Mahler-Lech theorem for non-linear recurrences and for fields of non-zero characteristic. We also describe two recent directions of progress toward showing decidability of the Skolem Problem subject to classical number theoretic conjectures.
The first new development concerns a recent algorithm [Y. Bilu et al., 2022] that decides the problem on the class of simple LRS (those with simple characteristic roots) subject to two classical conjectures about the exponential function. The algorithm is self-certifying: its output comes with a certificate of correctness that can be checked unconditionally. The two conjectures alluded to above are required for the proof of termination of the algorithm.
A second new development concerns the notion of Universal Skolem Set [F. Luca et al., 2022]: a recursive set S of positive integers such that it is decidable whether a given non-degenerate linear recurrence sequence has a zero in S. Decidability of the Skolem Problem is equivalent to the assertion that ℕ is a Universal Skolem Set. In lieu of this one can ask whether there exists a Universal Skolem Set of density one. We will present a recent a construction of a Universal Skolem Set that has positive density unconditionally and has density one subject to the Bateman-Horn conjecture in number theory. The latter is a far-reaching generalisation of Hardy and Littlewood’s twin primes conjecture.
Cite as
James Worrell. The Skolem Landscape (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 5:1-5:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{worrell:LIPIcs.ICALP.2023.5,
author = {Worrell, James},
title = {{The Skolem Landscape}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {5:1--5:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.5},
URN = {urn:nbn:de:0030-drops-180573},
doi = {10.4230/LIPIcs.ICALP.2023.5},
annote = {Keywords: Automata, Formal Languages, Linear Recurrence Sequences}
}
Document
Track A: Algorithms, Complexity and Games
Optimal Decremental Connectivity in Non-Sparse Graphs
Abstract
We present a dynamic algorithm for maintaining the connected and 2-edge-connected components in an undirected graph subject to edge deletions. The algorithm is Monte-Carlo randomized and processes any sequence of edge deletions in O(m + n poly log n) total time. Interspersed with the deletions, it can answer queries whether any two given vertices currently belong to the same (2-edge-)connected component in constant time. Our result is based on a general Monte-Carlo randomized reduction from decremental c-edge-connectivity to a variant of fully-dynamic c-edge-connectivity on a sparse graph.
For non-sparse graphs with Ω(n poly log n) edges, our connectivity and 2-edge-connectivity algorithms handle all deletions in optimal linear total time, using existing algorithms for the respective fully-dynamic problems. This improves upon an O(m log (n² / m) + n poly log n)-time algorithm of Thorup [J.Alg. 1999], which runs in linear time only for graphs with Ω(n²) edges.
Our constant amortized cost for edge deletions in decremental connectivity in non-sparse graphs should be contrasted with an Ω(log n/log log n) worst-case time lower bound in the decremental setting [Alstrup, Husfeldt, and Rauhe FOCS'98] as well as an Ω(log n) amortized time lower-bound in the fully-dynamic setting [Patrascu and Demaine STOC'04].
Cite as
Anders Aamand, Adam Karczmarz, Jakub Łącki, Nikos Parotsidis, Peter M. R. Rasmussen, and Mikkel Thorup. Optimal Decremental Connectivity in Non-Sparse Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{aamand_et_al:LIPIcs.ICALP.2023.6,
author = {Aamand, Anders and Karczmarz, Adam and {\L}\k{a}cki, Jakub and Parotsidis, Nikos and Rasmussen, Peter M. R. and Thorup, Mikkel},
title = {{Optimal Decremental Connectivity in Non-Sparse Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {6:1--6:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.6},
URN = {urn:nbn:de:0030-drops-180581},
doi = {10.4230/LIPIcs.ICALP.2023.6},
annote = {Keywords: decremental connectivity, dynamic connectivity}
}
Document
Track A: Algorithms, Complexity and Games
On Range Summary Queries
Abstract
We study the query version of the approximate heavy hitter and quantile problems. In the former problem, the input is a parameter ε and a set P of n points in ℝ^d where each point is assigned a color from a set C, and the goal is to build a structure such that given any geometric range γ, we can efficiently find a list of approximate heavy hitters in γ∩P, i.e., colors that appear at least ε |γ∩P| times in γ∩P, as well as their frequencies with an additive error of ε |γ∩P|. In the latter problem, each point is assigned a weight from a totally ordered universe and the query must output a sequence S of 1+1/ε weights such that the i-th weight in S has approximate rank iε|γ∩P|, meaning, rank iε|γ∩P| up to an additive error of ε|γ∩P|. Previously, optimal results were only known in 1D [Wei and Yi, 2011] but a few sub-optimal methods were available in higher dimensions [Peyman Afshani and Zhewei Wei, 2017; Pankaj K. Agarwal et al., 2012].
We study the problems for two important classes of geometric ranges: 3D halfspace and 3D dominance queries. It is known that many other important queries can be reduced to these two, e.g., 1D interval stabbing or interval containment, 2D three-sided queries, 2D circular as well as 2D k-nearest neighbors queries. We consider the real RAM model of computation where integer registers of size w bits, w = Θ(log n), are also available. For dominance queries, we show optimal solutions for both heavy hitter and quantile problems: using linear space, we can answer both queries in time O(log n + 1/ε). Note that as the output size is 1/ε, after investing the initial O(log n) searching time, our structure takes on average O(1) time to find a heavy hitter or a quantile! For more general halfspace heavy hitter queries, the same optimal query time can be achieved by increasing the space by an extra log_w(1/ε) (resp. log log_w(1/ε)) factor in 3D (resp. 2D). By spending extra log^O(1)(1/ε) factors in both time and space, we can also support quantile queries.
We remark that it is hopeless to achieve a similar query bound for dimensions 4 or higher unless significant advances are made in the data structure side of theory of geometric approximations.
Cite as
Peyman Afshani, Pingan Cheng, Aniket Basu Roy, and Zhewei Wei. On Range Summary Queries. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{afshani_et_al:LIPIcs.ICALP.2023.7,
author = {Afshani, Peyman and Cheng, Pingan and Basu Roy, Aniket and Wei, Zhewei},
title = {{On Range Summary Queries}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {7:1--7:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.7},
URN = {urn:nbn:de:0030-drops-180590},
doi = {10.4230/LIPIcs.ICALP.2023.7},
annote = {Keywords: Computational Geometry, Range Searching, Random Sampling, Geometric Approximation, Data Structures and Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Stable Matching: Choosing Which Proposals to Make
Abstract
To guarantee all agents are matched in general, the classic Deferred Acceptance algorithm needs complete preference lists. In practice, preference lists are short, yet stable matching still works well. This raises two questions:
- Why does it work well?
- Which proposals should agents include in their preference lists?
We study these questions in a model, introduced by Lee [Lee, 2016], with preferences based on correlated cardinal utilities: these utilities are based on common public ratings of each agent together with individual private adjustments. Lee showed that for suitable utility functions, in large markets, with high probability, for most agents, all stable matchings yield similar valued utilities. By means of a new analysis, we strengthen Lee’s result, showing that in large markets, with high probability, for all but the agents with the lowest public ratings, all stable matchings yield similar valued utilities. We can then deduce that for all but the agents with the lowest public ratings, each agent has an easily identified length O(log n) preference list that includes all of its stable matches, addressing the second question above. We note that this identification uses an initial communication phase.
We extend these results to settings where the two sides have unequal numbers of agents, to many-to-one settings, e.g. employers and workers, and we also show the existence of an ε-Bayes-Nash equilibrium in which every agent makes relatively few proposals. These results all rely on a new technique for sidestepping the conditioning between the tentative matching events that occur over the course of a run of the Deferred Acceptance algorithm. We complement these theoretical results with an experimental study.
Cite as
Ishan Agarwal and Richard Cole. Stable Matching: Choosing Which Proposals to Make. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{agarwal_et_al:LIPIcs.ICALP.2023.8,
author = {Agarwal, Ishan and Cole, Richard},
title = {{Stable Matching: Choosing Which Proposals to Make}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {8:1--8:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.8},
URN = {urn:nbn:de:0030-drops-180603},
doi = {10.4230/LIPIcs.ICALP.2023.8},
annote = {Keywords: Stable matching, randomized analysis}
}
Document
Track A: Algorithms, Complexity and Games
Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player
Abstract
A (ϕ,ε)-expander decomposition of a graph G (with n vertices and m edges) is a partition of V into clusters V₁,…,V_k with conductance Φ(G[V_i]) ≥ ϕ, such that there are at most ε m inter-cluster edges. Such a decomposition plays a crucial role in many graph algorithms. We give a randomized Õ(m/ϕ) time algorithm for computing a (ϕ, ϕlog²n)-expander decomposition. This improves upon the (ϕ, ϕlog³n)-expander decomposition also obtained in Õ(m/ϕ) time by [Saranurak and Wang, SODA 2019] (SW) and brings the number of inter-cluster edges within logarithmic factor of optimal.
One crucial component of SW’s algorithm is a non-stop version of the cut-matching game of [Khandekar, Rao, Vazirani, JACM 2009] (KRV): The cut player does not stop when it gets from the matching player an unbalanced sparse cut, but continues to play on a trimmed part of the large side. The crux of our improvement is the design of a non-stop version of the cleverer cut player of [Orecchia, Schulman, Vazirani, Vishnoi, STOC 2008] (OSVV). The cut player of OSSV uses a more sophisticated random walk, a subtle potential function, and spectral arguments. Designing and analysing a non-stop version of this game was an explicit open question asked by SW.
Cite as
Daniel Agassy, Dani Dorfman, and Haim Kaplan. Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{agassy_et_al:LIPIcs.ICALP.2023.9,
author = {Agassy, Daniel and Dorfman, Dani and Kaplan, Haim},
title = {{Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {9:1--9:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.9},
URN = {urn:nbn:de:0030-drops-180619},
doi = {10.4230/LIPIcs.ICALP.2023.9},
annote = {Keywords: Exapander Decomposition, Cut-Matching Game}
}
Document
Track A: Algorithms, Complexity and Games
Locality in Online, Dynamic, Sequential, and Distributed Graph Algorithms
Abstract
In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the adversary presents the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each node we get to see its radius-T neighborhood before choosing the output. Instead of looking ahead in time, we have the power of looking around in space.
We compare the online-LOCAL model with three other models: the LOCAL model of distributed computing, where each node produces its output based on its radius-T neighborhood, the SLOCAL model, which is the sequential counterpart of LOCAL, and the dynamic-LOCAL model, where changes in the dynamic input graph only influence the radius-T neighborhood of the point of change.
The SLOCAL and dynamic-LOCAL models are sandwiched between the LOCAL and online-LOCAL models. In general, all four models are distinct, but we study in particular locally checkable labeling problems (LCLs), which is a family of graph problems extensively studied in the context of distributed graph algorithms. We prove that for LCL problems in paths, cycles, and rooted trees, all four models are roughly equivalent: the locality of any LCL problem falls in the same broad class - O(log* n), Θ(log n), or n^Θ(1) - in all four models. In particular, this result enables one to generalize prior lower-bound results from the LOCAL model to all four models, and it also allows one to simulate e.g. dynamic-LOCAL algorithms efficiently in the LOCAL model.
We also show that this equivalence does not hold in two-dimensional grids or general bipartite graphs. We provide an online-LOCAL algorithm with locality O(log n) for the 3-coloring problem in bipartite graphs - this is a problem with locality Ω(n^{1/2}) in the LOCAL model and Ω(n^{1/10}) in the SLOCAL model.
Cite as
Amirreza Akbari, Navid Eslami, Henrik Lievonen, Darya Melnyk, Joona Särkijärvi, and Jukka Suomela. Locality in Online, Dynamic, Sequential, and Distributed Graph Algorithms. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{akbari_et_al:LIPIcs.ICALP.2023.10,
author = {Akbari, Amirreza and Eslami, Navid and Lievonen, Henrik and Melnyk, Darya and S\"{a}rkij\"{a}rvi, Joona and Suomela, Jukka},
title = {{Locality in Online, Dynamic, Sequential, and Distributed Graph Algorithms}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {10:1--10:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.10},
URN = {urn:nbn:de:0030-drops-180627},
doi = {10.4230/LIPIcs.ICALP.2023.10},
annote = {Keywords: Online computation, spatial advice, distributed algorithms, computational complexity}
}
Document
Track A: Algorithms, Complexity and Games
An Efficient Algorithm for All-Pairs Bounded Edge Connectivity
Abstract
Our work concerns algorithms for a variant of Maximum Flow in unweighted graphs. In the All-Pairs Connectivity (APC) problem, we are given a graph G on n vertices and m edges, and are tasked with computing the maximum number of edge-disjoint paths from s to t (equivalently, the size of a minimum (s,t)-cut) in G, for all pairs of vertices (s,t). Over undirected graphs, it is known that APC can be solved in essentially optimal n^{2+o(1)} time. In contrast, the true time complexity of APC over directed graphs remains open: this problem can be solved in Õ(m^ω) time, where ω ∈ [2, 2.373) is the exponent of matrix multiplication, but no matching conditional lower bound is known.
Following [Abboud et al., ICALP 2019], we study a bounded version of APC called the k-Bounded All Pairs Connectivity (k-APC) problem. In this variant of APC, we are given an integer k in addition to the graph G, and are now tasked with reporting the size of a minimum (s,t)-cut only for pairs (s,t) of vertices with min-cut value less than k (if the minimum (s,t)-cut has size at least k, we can just report it is "large" instead of computing the exact value).
Our main result is an Õ((kn)^ω) time algorithm solving k-APC in directed graphs. This is the first algorithm which solves k-APC faster than simply solving the more general APC problem exactly, for all k ≥ 3. This runtime is Õ(n^ω) for all k ≤ poly(log n), which essentially matches the optimal runtime for the k = 1 case of k-APC, under popular conjectures from fine-grained complexity. Previously, this runtime was only achieved for general directed graphs when k ≤ 2 [Georgiadis et al., ICALP 2017]. Our result employs the same algebraic framework used in previous work, introduced by [Cheung, Lau, and Leung, FOCS 2011]. A direct implementation of this framework involves inverting a large random matrix. Our new algorithm is based off the insight that for solving k-APC, it suffices to invert a low-rank random matrix instead of a generic random matrix.
We also obtain a new algorithm for a variant of k-APC, the k-Bounded All-Pairs Vertex Connectivity (k-APVC) problem, where for every pair of vertices (s,t), we are now tasked with reporting the maximum number of internally vertex-disjoint (rather than edge-disjoint) paths from s to t if this number is less than k, and otherwise reporting that this number is at least k.
Our second result is an Õ(k²n^ω) time algorithm solving k-APVC in directed graphs. Previous work showed how to solve an easier version of the k-APVC problem (where answers only need to be returned for pairs of vertices (s,t) which are not edges in the graph) in Õ((kn)^ω) time [Abboud et al, ICALP 2019]. In comparison, our algorithm solves the full k-APVC problem, and is faster if ω > 2.
Cite as
Shyan Akmal and Ce Jin. An Efficient Algorithm for All-Pairs Bounded Edge Connectivity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{akmal_et_al:LIPIcs.ICALP.2023.11,
author = {Akmal, Shyan and Jin, Ce},
title = {{An Efficient Algorithm for All-Pairs Bounded Edge Connectivity}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {11:1--11:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.11},
URN = {urn:nbn:de:0030-drops-180632},
doi = {10.4230/LIPIcs.ICALP.2023.11},
annote = {Keywords: maximum flow, all-pairs, connectivity, matrix rank}
}
Document
Track A: Algorithms, Complexity and Games
Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization
Abstract
A recent breakthrough work of Limaye, Srinivasan and Tavenas [Nutan Limaye et al., 2021] proved superpolynomial lower bounds for low-depth arithmetic circuits via a "hardness escalation" approach: they proved lower bounds for low-depth set-multilinear circuits and then lifted the bounds to low-depth general circuits. In this work, we prove superpolynomial lower bounds for low-depth circuits by bypassing the hardness escalation, i.e., the set-multilinearization, step. As set-multilinearization comes with an exponential blow-up in circuit size, our direct proof opens up the possibility of proving an exponential lower bound for low-depth homogeneous circuits by evading a crucial bottleneck. Our bounds hold for the iterated matrix multiplication and the Nisan-Wigderson design polynomials. We also define a subclass of unrestricted depth homogeneous formulas which we call unique parse tree (UPT) formulas, and prove superpolynomial lower bounds for these. This significantly generalizes the superpolynomial lower bounds for regular formulas [Neeraj Kayal et al., 2014; Hervé Fournier et al., 2015].
Cite as
Prashanth Amireddy, Ankit Garg, Neeraj Kayal, Chandan Saha, and Bhargav Thankey. Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{amireddy_et_al:LIPIcs.ICALP.2023.12,
author = {Amireddy, Prashanth and Garg, Ankit and Kayal, Neeraj and Saha, Chandan and Thankey, Bhargav},
title = {{Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {12:1--12:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.12},
URN = {urn:nbn:de:0030-drops-180642},
doi = {10.4230/LIPIcs.ICALP.2023.12},
annote = {Keywords: arithmetic circuits, low-depth circuits, lower bounds, shifted partials}
}
Document
Track A: Algorithms, Complexity and Games
Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering
Abstract
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a binary tree (i.e., Hierarchical Clustering). Points which are close in the metric space should be mapped to close points/leaves in the line/tree; similarly, points which are far in the metric space should be far in the line or on the tree. In particular we consider the Maximum Linear Arrangement problem [Refael Hassin and Shlomi Rubinstein, 2001] and the Maximum Hierarchical Clustering problem [Vincent Cohen-Addad et al., 2018] applied to metrics.
We design approximation schemes (1-ε approximation for any constant ε > 0) for these objectives. In particular this shows that by considering metrics one may significantly improve former approximations (0.5 for Max Linear Arrangement and 0.74 for Max Hierarchical Clustering). Our main technique, which is called multi-layer peeling, consists of recursively peeling off points which are far from the "core" of the metric space. The recursion ends once the core becomes a sufficiently densely weighted metric space (i.e. the average distance is at least a constant times the diameter) or once it becomes negligible with respect to its inner contribution to the objective. Interestingly, the algorithm in the Linear Arrangement case is much more involved than that in the Hierarchical Clustering case, and uses a significantly more delicate peeling.
Cite as
Yossi Azar and Danny Vainstein. Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{azar_et_al:LIPIcs.ICALP.2023.13,
author = {Azar, Yossi and Vainstein, Danny},
title = {{Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {13:1--13:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.13},
URN = {urn:nbn:de:0030-drops-180656},
doi = {10.4230/LIPIcs.ICALP.2023.13},
annote = {Keywords: Hierarchical clustering, Linear arrangements, Metric embeddings}
}
Document
Track A: Algorithms, Complexity and Games
Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation
Abstract
We study the robust communication complexity of maximum matching. Edges of an arbitrary n-vertex graph G are randomly partitioned between Alice and Bob independently and uniformly. Alice has to send a single message to Bob such that Bob can find an (approximate) maximum matching of the whole graph G. We specifically study the best approximation ratio achievable via protocols where Alice communicates only Õ(n) bits to Bob.
There has been a growing interest on the robust communication model due to its connections to the random-order streaming model. An algorithm of Assadi and Behnezhad [ICALP'21] implies a (2/3+ε₀ ∼ .667)-approximation for a small constant 0 < ε₀ < 10^{-18}, which remains the best-known approximation for general graphs. For bipartite graphs, Assadi and Behnezhad [Random'21] improved the approximation to .716 albeit with a computationally inefficient (i.e., exponential time) protocol.
In this paper, we study a natural and efficient protocol implied by a random-order streaming algorithm of Bernstein [ICALP'20] which is based on edge-degree constrained subgraphs (EDCS) [Bernstein and Stein; ICALP'15]. The result of Bernstein immediately implies that this protocol achieves an (almost) (2/3 ∼ .666)-approximation in the robust communication model. We present a new analysis, proving that it achieves a much better (almost) (5/6 ∼ .833)-approximation. This significantly improves previous approximations both for general and bipartite graphs. We also prove that our analysis of Bernstein’s protocol is tight.
Cite as
Amir Azarmehr and Soheil Behnezhad. Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{azarmehr_et_al:LIPIcs.ICALP.2023.14,
author = {Azarmehr, Amir and Behnezhad, Soheil},
title = {{Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {14:1--14:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.14},
URN = {urn:nbn:de:0030-drops-180666},
doi = {10.4230/LIPIcs.ICALP.2023.14},
annote = {Keywords: Maximum Matching, Robust Communication Complexity, Edge Degree Constrained Subgraph}
}
Document
Track A: Algorithms, Complexity and Games
Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions
Abstract
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Combinatorica 15(3):435-454, 1995). Williamson et al. prove an approximation ratio of two for connectivity augmentation problems where the connectivity requirements can be specified by uncrossable functions. They state: "Extending our algorithm to handle non-uncrossable functions remains a challenging open problem. The key feature of uncrossable functions is that there exists an optimal dual solution which is laminar... A larger open issue is to explore further the power of the primal-dual approach for obtaining approximation algorithms for other combinatorial optimization problems."
Our main result proves a 16-approximation ratio via the primal-dual method for a class of functions that generalizes the notion of an uncrossable function. There exist instances that can be handled by our methods where none of the optimal dual solutions have a laminar support.
We present applications of our main result to three network-design problems.
1) A 16-approximation algorithm for augmenting the family of small cuts of a graph G. The previous best approximation ratio was O(log |V(G)|).
2) A 16⋅⌈k/u_min⌉-approximation algorithm for the Cap-k-ECSS problem which is as follows: Given an undirected graph G = (V,E) with edge costs c ∈ ℚ_{≥0}^E and edge capacities u ∈ ℤ_{≥0}^E, find a minimum cost subset of the edges F ⊆ E such that the capacity across any cut in (V,F) is at least k; u_min (respectively, u_max) denote the minimum (respectively, maximum) capacity of an edge in E, and w.l.o.g. u_max ≤ k. The previous best approximation ratio was min(O(log|V|), k, 2u_max).
3) A 20-approximation algorithm for the model of (p,2)-Flexible Graph Connectivity. The previous best approximation ratio was O(log|V(G)|), where G denotes the input graph.
Cite as
Ishan Bansal, Joseph Cheriyan, Logan Grout, and Sharat Ibrahimpur. Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bansal_et_al:LIPIcs.ICALP.2023.15,
author = {Bansal, Ishan and Cheriyan, Joseph and Grout, Logan and Ibrahimpur, Sharat},
title = {{Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {15:1--15:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.15},
URN = {urn:nbn:de:0030-drops-180678},
doi = {10.4230/LIPIcs.ICALP.2023.15},
annote = {Keywords: Approximation algorithms, Edge-connectivity of graphs, f-Connectivity problem, Flexible Graph Connectivity, Minimum cuts, Network design, Primal-dual method, Small cuts}
}
Document
Track A: Algorithms, Complexity and Games
Approximation Algorithms for Envy-Free Cake Division with Connected Pieces
Abstract
Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece of the cake, we develop approximation algorithms for finding envy-free (fair) cake divisions. In particular, this work improves the state-of-the-art additive approximation bound for this fundamental problem. Our results hold for general cake division instances in which the agents' valuations satisfy basic assumptions and are normalized (to have value 1 for the cake). Furthermore, the developed algorithms execute in polynomial time under the standard Robertson-Webb query model.
Prior work has shown that one can efficiently compute a cake division (with connected pieces) in which the additive envy of any agent is at most 1/3. An efficient algorithm is also known for finding connected cake divisions that are (almost) 1/2-multiplicatively envy-free. Improving the additive approximation guarantee and maintaining the multiplicative one, we develop a polynomial-time algorithm that computes a connected cake division that is both (1/4 +o(1))-additively envy-free and (1/2 - o(1))-multiplicatively envy-free. Our algorithm is based on the ideas of interval growing and envy-cycle elimination.
In addition, we study cake division instances in which the number of distinct valuations across the agents is parametrically bounded. We show that such cake division instances admit a fully polynomial-time approximation scheme for connected envy-free cake division.
Cite as
Siddharth Barman and Pooja Kulkarni. Approximation Algorithms for Envy-Free Cake Division with Connected Pieces. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{barman_et_al:LIPIcs.ICALP.2023.16,
author = {Barman, Siddharth and Kulkarni, Pooja},
title = {{Approximation Algorithms for Envy-Free Cake Division with Connected Pieces}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {16:1--16:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.16},
URN = {urn:nbn:de:0030-drops-180685},
doi = {10.4230/LIPIcs.ICALP.2023.16},
annote = {Keywords: Fair Division, Envy-Freeness, Envy-Cycle Elimination}
}
Document
Track A: Algorithms, Complexity and Games
Cumulative Memory Lower Bounds for Randomized and Quantum Computation
Abstract
Cumulative memory - the sum of space used per step over the duration of a computation - is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more accurate cost measure for algorithms that have infrequent spikes in memory usage and are run in environments such as cloud computing that allow dynamic allocation and de-allocation of resources during execution, or when many multiple instances of an algorithm are interleaved in parallel.
We prove the first lower bounds on cumulative memory complexity for both sequential classical computation and quantum circuits. Moreover, we develop general paradigms for bounding cumulative memory complexity inspired by the standard paradigms for proving time-space tradeoff lower bounds that can only lower bound the maximum space used during an execution. The resulting lower bounds on cumulative memory that we obtain are just as strong as the best time-space tradeoff lower bounds, which are very often known to be tight.
Although previous results for pebbling and random oracle models have yielded time-space tradeoff lower bounds larger than the cumulative memory complexity, our results show that in general computational models such separations cannot follow from known lower bound techniques and are not true for many functions.
Among many possible applications of our general methods, we show that any classical sorting algorithm with success probability at least 1/poly(n) requires cumulative memory ̃ Ω(n²), any classical matrix multiplication algorithm requires cumulative memory Ω(n⁶/T), any quantum sorting circuit requires cumulative memory Ω(n³/T), and any quantum circuit that finds k disjoint collisions in a random function requires cumulative memory Ω(k³n/T²).
Cite as
Paul Beame and Niels Kornerup. Cumulative Memory Lower Bounds for Randomized and Quantum Computation. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{beame_et_al:LIPIcs.ICALP.2023.17,
author = {Beame, Paul and Kornerup, Niels},
title = {{Cumulative Memory Lower Bounds for Randomized and Quantum Computation}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {17:1--17:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.17},
URN = {urn:nbn:de:0030-drops-180694},
doi = {10.4230/LIPIcs.ICALP.2023.17},
annote = {Keywords: Cumulative memory complexity, time-space tradeoffs, branching programs, quantum lower bounds}
}
Document
Track A: Algorithms, Complexity and Games
Dynamic Averaging Load Balancing on Arbitrary Graphs
Abstract
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is averaged over the edges of that matching. We analyze the discrete case where load items are indivisible, moreover our results also carry over to the continuous case where load items can be split arbitrarily. For the choice of the matchings we consider three different models, random matchings of linear size, random matchings containing only single edges, and deterministic sequences of matchings covering the whole graph. We bound the discrepancy, which is defined as the difference between the maximum and the minimum load. Our results cover a broad range of graph classes and, to the best of our knowledge, our analysis is the first result for discrete and dynamic averaging load balancing processes. As our main technical contribution we develop a drift result that allows us to apply techniques based on the effective resistance in an electrical network to the setting of dynamic load balancing.
Cite as
Petra Berenbrink, Lukas Hintze, Hamed Hosseinpour, Dominik Kaaser, and Malin Rau. Dynamic Averaging Load Balancing on Arbitrary Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{berenbrink_et_al:LIPIcs.ICALP.2023.18,
author = {Berenbrink, Petra and Hintze, Lukas and Hosseinpour, Hamed and Kaaser, Dominik and Rau, Malin},
title = {{Dynamic Averaging Load Balancing on Arbitrary Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {18:1--18:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.18},
URN = {urn:nbn:de:0030-drops-180707},
doi = {10.4230/LIPIcs.ICALP.2023.18},
annote = {Keywords: Dynamic Load Balancing, Distributed Computing, Randomized Algorithms, Drift Analysis}
}
Document
Track A: Algorithms, Complexity and Games
Fast Approximation of Search Trees on Trees with Centroid Trees
Abstract
Search trees on trees (STTs) generalize the fundamental binary search tree (BST) data structure: in STTs the underlying search space is an arbitrary tree, whereas in BSTs it is a path. An optimal BST of size n can be computed for a given distribution of queries in 𝒪(n²) time [Knuth, Acta Inf. 1971] and centroid BSTs provide a nearly-optimal alternative, computable in 𝒪(n) time [Mehlhorn, SICOMP 1977].
By contrast, optimal STTs are not known to be computable in polynomial time, and the fastest constant-approximation algorithm runs in 𝒪(n³) time [Berendsohn, Kozma, SODA 2022]. Centroid trees can be defined for STTs analogously to BSTs, and they have been used in a wide range of algorithmic applications. In the unweighted case (i.e., for a uniform distribution of queries), the centroid tree can be computed in 𝒪(n) time [Brodal, Fagerberg, Pedersen, Östlin, ICALP 2001; Della Giustina, Prezza, Venturini, SPIRE 2019]. These algorithms, however, do not readily extend to the weighted case. Moreover, no approximation guarantees were previously known for centroid trees in either the unweighted or weighted cases.
In this paper we revisit centroid trees in a general, weighted setting, and we settle both the algorithmic complexity of constructing them, and the quality of their approximation. For constructing a weighted centroid tree, we give an output-sensitive 𝒪(n log h) ⊆ 𝒪(n log n) time algorithm, where h is the height of the resulting centroid tree. If the weights are of polynomial complexity, the running time is 𝒪(n log log n). We show these bounds to be optimal, in a general decision tree model of computation. For approximation, we prove that the cost of a centroid tree is at most twice the optimum, and this guarantee is best possible, both in the weighted and unweighted cases. We also give tight, fine-grained bounds on the approximation-ratio for bounded-degree trees and on the approximation-ratio of more general α-centroid trees.
Cite as
Benjamin Aram Berendsohn, Ishay Golinsky, Haim Kaplan, and László Kozma. Fast Approximation of Search Trees on Trees with Centroid Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{berendsohn_et_al:LIPIcs.ICALP.2023.19,
author = {Berendsohn, Benjamin Aram and Golinsky, Ishay and Kaplan, Haim and Kozma, L\'{a}szl\'{o}},
title = {{Fast Approximation of Search Trees on Trees with Centroid Trees}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {19:1--19:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.19},
URN = {urn:nbn:de:0030-drops-180711},
doi = {10.4230/LIPIcs.ICALP.2023.19},
annote = {Keywords: centroid tree, search trees on trees, approximation}
}
Document
Track A: Algorithms, Complexity and Games
Improved Product-State Approximation Algorithms for Quantum Local Hamiltonians
Abstract
The ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics, however, it is QMA-Hard to estimate them in general. In this paper, we develop new techniques to find classical, additive error product-state approximations for these quantities on certain families of Quantum k-Local Hamiltonians. Namely, those which are either dense, have low threshold rank, or are defined on a sparse graph that excludes a fixed minor, building on the methods and the systems studied by Brandão and Harrow, Gharibian and Kempe, and Bansal, Bravyi and Terhal.
We present two main technical contributions. First, we discuss a connection between product-state approximations of local Hamiltonians and combinatorial graph property testing. We develop a series of weak Szemerédi regularity lemmas for k-local Hamiltonians, built on those of Frieze and Kannan and others. We use them to develop constant time sampling algorithms, and to characterize the "vertex sample complexity" of the Local Hamiltonian problem, in an analog to a classical result by Alon, de la Vega, Kannan and Karpinski. Second, we build on the information-theoretic product-state approximation techniques by Brandão and Harrow, extending their results to the free energy and to an asymmetric graph setting. We leverage this structure to define families of algorithms for the free energy at low temperatures, and new algorithms for certain sparse graph families.
Cite as
Thiago Bergamaschi. Improved Product-State Approximation Algorithms for Quantum Local Hamiltonians. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bergamaschi:LIPIcs.ICALP.2023.20,
author = {Bergamaschi, Thiago},
title = {{Improved Product-State Approximation Algorithms for Quantum Local Hamiltonians}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {20:1--20:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.20},
URN = {urn:nbn:de:0030-drops-180722},
doi = {10.4230/LIPIcs.ICALP.2023.20},
annote = {Keywords: Approximation Algorithms, Quantum Information}
}
Document
Track A: Algorithms, Complexity and Games
Sublinear Time Eigenvalue Approximation via Random Sampling
Abstract
We study the problem of approximating the eigenspectrum of a symmetric matrix A ∈ ℝ^{n×n} with bounded entries (i.e., ‖A‖_∞ ≤ 1). We present a simple sublinear time algorithm that approximates all eigenvalues of A up to additive error ±εn using those of a randomly sampled Õ((log³ n)/ε³)×Õ((log³ n)/ε³) principal submatrix. Our result can be viewed as a concentration bound on the complete eigenspectrum of a random submatrix, significantly extending known bounds on just the singular values (the magnitudes of the eigenvalues). We give improved error bounds of ± ε √{nnz(A)} and ±ε‖A‖_F when the rows of A can be sampled with probabilities proportional to their sparsities or their squared 𝓁₂ norms respectively. Here nnz(A) is the number of non-zero entries in A and ‖A‖_F is its Frobenius norm. Even for the strictly easier problems of approximating the singular values or testing the existence of large negative eigenvalues (Bakshi, Chepurko, and Jayaram, FOCS '20), our results are the first that take advantage of non-uniform sampling to give improved error bounds. From a technical perspective, our results require several new eigenvalue concentration and perturbation bounds for matrices with bounded entries. Our non-uniform sampling bounds require a new algorithmic approach, which judiciously zeroes out entries of a randomly sampled submatrix to reduce variance, before computing the eigenvalues of that submatrix as estimates for those of A. We complement our theoretical results with numerical simulations, which demonstrate the effectiveness of our algorithms in practice.
Cite as
Rajarshi Bhattacharjee, Gregory Dexter, Petros Drineas, Cameron Musco, and Archan Ray. Sublinear Time Eigenvalue Approximation via Random Sampling. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bhattacharjee_et_al:LIPIcs.ICALP.2023.21,
author = {Bhattacharjee, Rajarshi and Dexter, Gregory and Drineas, Petros and Musco, Cameron and Ray, Archan},
title = {{Sublinear Time Eigenvalue Approximation via Random Sampling}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {21:1--21:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.21},
URN = {urn:nbn:de:0030-drops-180733},
doi = {10.4230/LIPIcs.ICALP.2023.21},
annote = {Keywords: sublinear algorithms, eigenvalue approximation, randomized linear algebra}
}
Document
Track A: Algorithms, Complexity and Games
Streaming k-Edit Approximate Pattern Matching via String Decomposition
Abstract
In this paper we give an algorithm for streaming k-edit approximate pattern matching which uses space Õ(k²) and time Õ(k²) per arriving symbol. This improves substantially on the recent algorithm of Kociumaka, Porat and Starikovskaya [Kociumaka et al., 2022] which uses space Õ(k⁵) and time Õ(k⁸) per arriving symbol. In the k-edit approximate pattern matching problem we get a pattern P and text T and we want to identify all substrings of the text T that are at edit distance at most k from P. In the streaming version of this problem both the pattern and the text arrive in a streaming fashion symbol by symbol and after each symbol of the text we need to report whether there is a current suffix of the text with edit distance at most k from P. We measure the total space needed by the algorithm and time needed per arriving symbol.
Cite as
Sudatta Bhattacharya and Michal Koucký. Streaming k-Edit Approximate Pattern Matching via String Decomposition. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bhattacharya_et_al:LIPIcs.ICALP.2023.22,
author = {Bhattacharya, Sudatta and Kouck\'{y}, Michal},
title = {{Streaming k-Edit Approximate Pattern Matching via String Decomposition}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {22:1--22:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.22},
URN = {urn:nbn:de:0030-drops-180741},
doi = {10.4230/LIPIcs.ICALP.2023.22},
annote = {Keywords: Approximate pattern matching, edit distance, streaming algorithms}
}
Document
Track A: Algorithms, Complexity and Games
On Computing the Vertex Connectivity of 1-Plane Graphs
Abstract
A graph is called 1-plane if it has an embedding in the plane where each edge is crossed at most once by another edge. A crossing of a 1-plane graph is called an ×-crossing if there are no other edges connecting the endpoints of the crossing (apart from the crossing pair of edges). In this paper, we show how to compute the vertex connectivity of a 1-plane graph G without ×-crossings in linear time.
To do so, we show that for any two vertices u,v in a minimum separating set S, the distance between u and v in an auxiliary graph Λ(G) (obtained by planarizing G and then inserting into each face a new vertex adjacent to all vertices of the face) is small. It hence suffices to search for a minimum separating set in various subgraphs Λ_i of Λ(G) with small diameter. Since Λ(G) is planar, the subgraphs Λ_i have small treewidth. Each minimum separating set S then gives rise to a partition of Λ_i into three vertex sets with special properties; such a partition can be found via Courcelle’s theorem in linear time.
Cite as
Therese Biedl and Karthik Murali. On Computing the Vertex Connectivity of 1-Plane Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{biedl_et_al:LIPIcs.ICALP.2023.23,
author = {Biedl, Therese and Murali, Karthik},
title = {{On Computing the Vertex Connectivity of 1-Plane Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {23:1--23:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.23},
URN = {urn:nbn:de:0030-drops-180753},
doi = {10.4230/LIPIcs.ICALP.2023.23},
annote = {Keywords: 1-Planar Graph, Connectivity, Linear Time, Treewidth}
}
Document
Track A: Algorithms, Complexity and Games
Fault-Tolerant ST-Diameter Oracles
Abstract
We study the problem of estimating the ST-diameter of a graph that is subject to a bounded number of edge failures. An f-edge fault-tolerant ST-diameter oracle (f-FDO-ST) is a data structure that preprocesses a given graph G, two sets of vertices S,T, and positive integer f. When queried with a set F of at most f edges, the oracle returns an estimate D̂ of the ST-diameter diam(G-F,S,T), the maximum distance between vertices in S and T in G-F. The oracle has stretch σ ⩾ 1 if diam(G-F,S,T) ⩽ D̂ ⩽ σ diam(G-F,S,T). If S and T both contain all vertices, the data structure is called an f-edge fault-tolerant diameter oracle (f-FDO). An f-edge fault-tolerant distance sensitivity oracles (f-DSO) estimates the pairwise graph distances under up to f failures.
We design new f-FDOs and f-FDO-STs by reducing their construction to that of all-pairs and single-source f-DSOs. We obtain several new tradeoffs between the size of the data structure, stretch guarantee, query and preprocessing times for diameter oracles by combining our black-box reductions with known results from the literature.
We also provide an information-theoretic lower bound on the space requirement of approximate f-FDOs. We show that there exists a family of graphs for which any f-FDO with sensitivity f ⩾ 2 and stretch less than 5/3 requires Ω(n^{3/2}) bits of space, regardless of the query time.
Cite as
Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Simon Krogmann, and Martin Schirneck. Fault-Tolerant ST-Diameter Oracles. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bilo_et_al:LIPIcs.ICALP.2023.24,
author = {Bil\`{o}, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin},
title = {{Fault-Tolerant ST-Diameter Oracles}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {24:1--24:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.24},
URN = {urn:nbn:de:0030-drops-180762},
doi = {10.4230/LIPIcs.ICALP.2023.24},
annote = {Keywords: diameter oracles, distance sensitivity oracles, space lower bounds, fault-tolerant data structures}
}
Document
Track A: Algorithms, Complexity and Games
Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing
Abstract
We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions f:{0,1}^d → ℝ. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function f over an arbitrary partially ordered domain as a collection of Boolean functions over the same domain, roughly capturing the distance of f to monotonicity and the structure of violations of f to monotonicity.
We apply our generalized isoperimetric inequality to improve algorithms for testing monotonicity and approximating the distance to monotonicity for real-valued functions. Our tester for monotonicity has query complexity Õ(min(r √d,d)), where r is the size of the image of the input function. (The best previously known tester makes O(d) queries, as shown by Chakrabarty and Seshadhri (STOC 2013).) Our tester is nonadaptive and has 1-sided error. We prove a matching lower bound for nonadaptive, 1-sided error testers for monotonicity. We also show that the distance to monotonicity of real-valued functions that are α-far from monotone can be approximated nonadaptively within a factor of O(√{d log d}) with query complexity polynomial in 1/α and the dimension d. This query complexity is known to be nearly optimal for nonadaptive algorithms even for the special case of Boolean functions. (The best previously known distance approximation algorithm for real-valued functions, by Fattal and Ron (TALG 2010) achieves O(d log r)-approximation.)
Cite as
Hadley Black, Iden Kalemaj, and Sofya Raskhodnikova. Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{black_et_al:LIPIcs.ICALP.2023.25,
author = {Black, Hadley and Kalemaj, Iden and Raskhodnikova, Sofya},
title = {{Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {25:1--25:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.25},
URN = {urn:nbn:de:0030-drops-180774},
doi = {10.4230/LIPIcs.ICALP.2023.25},
annote = {Keywords: Isoperimetric inequalities, property testing, monotonicity testing}
}
Document
Track A: Algorithms, Complexity and Games
The Geometry of Tree-Based Sorting
Abstract
We study the connections between sorting and the binary search tree (BST) model, with an aim towards showing that the fields are connected more deeply than is currently appreciated. While any BST can be used to sort by inserting the keys one-by-one, this is a very limited relationship and importantly says nothing about parallel sorting. We show what we believe to be the first formal relationship between the BST model and sorting. Namely, we show that a large class of sorting algorithms, which includes mergesort, quicksort, insertion sort, and almost every instance-optimal sorting algorithm, are equivalent in cost to offline BST algorithms. Our main theoretical tool is the geometric interpretation of the BST model introduced by Demaine et al. [Demaine et al., 2009], which finds an equivalence between searches on a BST and point sets in the plane satisfying a certain property. To give an example of the utility of our approach, we introduce the log-interleave bound, a measure of the information-theoretic complexity of a permutation π, which is within a lg lg n multiplicative factor of a known lower bound in the BST model; we also devise a parallel sorting algorithm with polylogarithmic span that sorts a permutation π using comparisons proportional to its log-interleave bound. Our aforementioned result on sorting and offline BST algorithms can be used to show existence of an offline BST algorithm whose cost is within a constant factor of the log-interleave bound of any permutation π.
Cite as
Guy E. Blelloch and Magdalen Dobson. The Geometry of Tree-Based Sorting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{blelloch_et_al:LIPIcs.ICALP.2023.26,
author = {Blelloch, Guy E. and Dobson, Magdalen},
title = {{The Geometry of Tree-Based Sorting}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {26:1--26:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.26},
URN = {urn:nbn:de:0030-drops-180780},
doi = {10.4230/LIPIcs.ICALP.2023.26},
annote = {Keywords: binary search trees, sorting, dynamic optimality, parallelism}
}
Document
Track A: Algorithms, Complexity and Games
Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters
Abstract
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:
- Binary CSP parameterized by the vertex cover number is W[3]-complete. More generally, for every positive integer d, Binary CSP parameterized by the size of a modulator to a treedepth-d graph is W[2d+1]-complete. This provides a new family of natural problems that are complete for odd levels of the W-hierarchy.
- We introduce a new complexity class XSLP, defined so that Binary CSP parameterized by treedepth is complete for this class. We provide two equivalent characterizations of XSLP: the first one relates XSLP to a model of an alternating Turing machine with certain restrictions on conondeterminism and space complexity, while the second one links XSLP to the problem of model-checking first-order logic with suitably restricted universal quantification. Interestingly, the proof of the machine characterization of XSLP uses the concept of universal trees, which are prominently featured in the recent work on parity games.
- We describe a new complexity hierarchy sandwiched between the W-hierarchy and the A-hierarchy: For every odd t, we introduce a parameterized complexity class S[t] with W[t] ⊆ S[t] ⊆ A[t], defined using a parameter that interpolates between the vertex cover number and the treedepth. We expect that many of the studied classes will be useful in the future for pinpointing the complexity of various structural parameterizations of graph problems.
Cite as
Hans L. Bodlaender, Carla Groenland, and Michał Pilipczuk. Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bodlaender_et_al:LIPIcs.ICALP.2023.27,
author = {Bodlaender, Hans L. and Groenland, Carla and Pilipczuk, Micha{\l}},
title = {{Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {27:1--27:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.27},
URN = {urn:nbn:de:0030-drops-180798},
doi = {10.4230/LIPIcs.ICALP.2023.27},
annote = {Keywords: Parameterized Complexity, Constraint Satisfaction Problems, Binary CSP, List Coloring, Vertex Cover, Treedepth, W-hierarchy}
}
Document
Track A: Algorithms, Complexity and Games
Nondeterministic Interactive Refutations for Nearest Boolean Vector
Abstract
Most n-dimensional subspaces 𝒜 of ℝ^m are Ω(√m)-far from the Boolean cube {-1, 1}^m when n < cm for some constant c > 0. How hard is it to certify that the Nearest Boolean Vector (NBV) is at least γ √m far from a given random 𝒜?
Certifying NBV instances is relevant to the computational complexity of approximating the Sherrington-Kirkpatrick Hamiltonian, i.e. maximizing x^TAx over the Boolean cube for a matrix A sampled from the Gaussian Orthogonal Ensemble. The connection was discovered by Mohanty, Raghavendra, and Xu (STOC 2020). Improving on their work, Ghosh, Jeronimo, Jones, Potechin, and Rajendran (FOCS 2020) showed that certification is not possible in the sum-of-squares framework when m ≪ n^1.5, even with distance γ = 0.
We present a non-deterministic interactive certification algorithm for NBV when m ≫ n log n and γ ≪ 1/mn^1.5. The algorithm is obtained by adapting a public-key encryption scheme of Ajtai and Dwork.
Cite as
Andrej Bogdanov and Alon Rosen. Nondeterministic Interactive Refutations for Nearest Boolean Vector. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bogdanov_et_al:LIPIcs.ICALP.2023.28,
author = {Bogdanov, Andrej and Rosen, Alon},
title = {{Nondeterministic Interactive Refutations for Nearest Boolean Vector}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {28:1--28:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.28},
URN = {urn:nbn:de:0030-drops-180801},
doi = {10.4230/LIPIcs.ICALP.2023.28},
annote = {Keywords: average-case complexity, statistical zero-knowledge, nondeterministic refutation, Sherrington-Kirkpatrick Hamiltonian, complexity of statistical inference, lattice smoothing}
}
Document
Track A: Algorithms, Complexity and Games
A 4/3 Approximation for 2-Vertex-Connectivity
Abstract
The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph G. Our goal is to find a subgraph S of G with the minimum number of edges which is 2-vertex-connected, namely S remains connected after the deletion of an arbitrary node. 2VCSS is well-studied in terms of approximation algorithms, and the current best (polynomial-time) approximation factor is 10/7 by Heeger and Vygen [SIDMA'17] (improving on earlier results by Khuller and Vishkin [STOC'92] and Garg, Vempala and Singla [SODA'93]).
Here we present an improved 4/3 approximation. Our main technical ingredient is an approximation preserving reduction to a conveniently structured subset of instances which are "almost" 3-vertex-connected. The latter reduction might be helpful in future work.
Cite as
Miguel Bosch-Calvo, Fabrizio Grandoni, and Afrouz Jabal Ameli. A 4/3 Approximation for 2-Vertex-Connectivity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{boschcalvo_et_al:LIPIcs.ICALP.2023.29,
author = {Bosch-Calvo, Miguel and Grandoni, Fabrizio and Jabal Ameli, Afrouz},
title = {{A 4/3 Approximation for 2-Vertex-Connectivity}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {29:1--29:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.29},
URN = {urn:nbn:de:0030-drops-180813},
doi = {10.4230/LIPIcs.ICALP.2023.29},
annote = {Keywords: Algorithm, Network Design, Vertex-Connectivity, Approximation}
}
Document
Track A: Algorithms, Complexity and Games
Lower Bounds for Pseudo-Deterministic Counting in a Stream
Abstract
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary - for many streaming problems, both relaxations must be employed simultaneously, to avoid an exponentially larger (and often trivial) space complexity. A common drawback of these randomized approximate algorithms is that independent executions on the same input have different outputs, that depend on their random coins. Pseudo-deterministic algorithms combat this issue, and for every input, they output with high probability the same "canonical" solution.
We consider perhaps the most basic problem in data streams, of counting the number of items in a stream of length at most n. Morris’s counter [CACM, 1978] is a randomized approximation algorithm for this problem that uses O(log log n) bits of space, for every fixed approximation factor (greater than 1). Goldwasser, Grossman, Mohanty and Woodruff [ITCS 2020] asked whether pseudo-deterministic approximation algorithms can match this space complexity. Our main result answers their question negatively, and shows that such algorithms must use Ω(√{log n / log log n}) bits of space.
Our approach is based on a problem that we call Shift Finding, and may be of independent interest. In this problem, one has query access to a shifted version of a known string F ∈ {0,1}^{3n}, which is guaranteed to start with n zeros and end with n ones, and the goal is to find the unknown shift using a small number of queries. We provide for this problem an algorithm that uses O(√n) queries. It remains open whether poly(log n) queries suffice; if true, then our techniques immediately imply a nearly-tight Ω(log n/log log n) space bound for pseudo-deterministic approximate counting.
Cite as
Vladimir Braverman, Robert Krauthgamer, Aditya Krishnan, and Shay Sapir. Lower Bounds for Pseudo-Deterministic Counting in a Stream. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{braverman_et_al:LIPIcs.ICALP.2023.30,
author = {Braverman, Vladimir and Krauthgamer, Robert and Krishnan, Aditya and Sapir, Shay},
title = {{Lower Bounds for Pseudo-Deterministic Counting in a Stream}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {30:1--30:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.30},
URN = {urn:nbn:de:0030-drops-180827},
doi = {10.4230/LIPIcs.ICALP.2023.30},
annote = {Keywords: streaming algorithms, pseudo-deterministic, approximate counting}
}
Document
Track A: Algorithms, Complexity and Games
Minimum Chain Cover in Almost Linear Time
Abstract
A minimum chain cover (MCC) of a k-width directed acyclic graph (DAG) G = (V, E) is a set of k chains (paths in the transitive closure) of G such that every vertex appears in at least one chain in the cover. The state-of-the-art solutions for MCC run in time Õ(k(|V|+|E|)) [Mäkinen et at., TALG], O(T_{MF}(|E|) + k|V|), O(k²|V| + |E|) [Cáceres et al., SODA 2022], Õ(|V|^{3/2} + |E|) [Kogan and Parter, ICALP 2022] and Õ(T_{MCF}(|E|) + √k|V|) [Kogan and Parter, SODA 2023], where T_{MF}(|E|) and T_{MCF}(|E|) are the running times for solving maximum flow (MF) and minimum-cost flow (MCF), respectively.
In this work we present an algorithm running in time O(T_{MF}(|E|) + (|V|+|E|)log k). By considering the recent result for solving MF [Chen et al., FOCS 2022] our algorithm is the first running in almost linear time. Moreover, our techniques are deterministic and derive a deterministic near-linear time algorithm for MCC if the same is provided for MF. At the core of our solution we use a modified version of the mergeable dictionaries [Farach and Thorup, Algorithmica], [Iacono and Özkan, ICALP 2010] data structure boosted with the SIZE-SPLIT operation and answering queries in amortized logarithmic time, which can be of independent interest.
Cite as
Manuel Cáceres. Minimum Chain Cover in Almost Linear Time. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 31:1-31:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{caceres:LIPIcs.ICALP.2023.31,
author = {C\'{a}ceres, Manuel},
title = {{Minimum Chain Cover in Almost Linear Time}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {31:1--31:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.31},
URN = {urn:nbn:de:0030-drops-180834},
doi = {10.4230/LIPIcs.ICALP.2023.31},
annote = {Keywords: Minimum chain cover, directed acyclic graph, minimum flow, flow decomposition, mergeable dictionaries, amortized running time}
}
Document
Track A: Algorithms, Complexity and Games
Improved Hardness Results for the Guided Local Hamiltonian Problem
Abstract
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has fidelity (inverse-polynomially) close to 1/2 with a ground state.
In this paper, we optimally improve both the locality and the fidelity parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has fidelity (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. Beyond the hardness of estimating the ground state energy, we also show BQP-hardness persists when considering estimating energies of excited states of these Hamiltonians instead. Those make further steps towards establishing practical quantum advantage in quantum chemistry.
Cite as
Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, and Jordi Weggemans. Improved Hardness Results for the Guided Local Hamiltonian Problem. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cade_et_al:LIPIcs.ICALP.2023.32,
author = {Cade, Chris and Folkertsma, Marten and Gharibian, Sevag and Hayakawa, Ryu and Le Gall, Fran\c{c}ois and Morimae, Tomoyuki and Weggemans, Jordi},
title = {{Improved Hardness Results for the Guided Local Hamiltonian Problem}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {32:1--32:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.32},
URN = {urn:nbn:de:0030-drops-180840},
doi = {10.4230/LIPIcs.ICALP.2023.32},
annote = {Keywords: Quantum computing, Quantum advantage, Quantum Chemistry, Guided Local Hamiltonian Problem}
}
Document
Track A: Algorithms, Complexity and Games
Planar #CSP Equality Corresponds to Quantum Isomorphism - A Holant Viewpoint
Abstract
Recently, Mančinska and Roberson proved [Mančinska and Roberson, 2020] that two graphs G and G' are quantum isomorphic if and only if they admit the same number of homomorphisms from all planar graphs. We extend this result to planar #CSP with any pair of sets ℱ and ℱ' of real-valued, arbitrary-arity constraint functions. Graph homomorphism is the special case where each of ℱ and ℱ' contains a single symmetric 0-1-valued binary constraint function. Our treatment uses the framework of planar Holant problems. To prove that quantum isomorphic constraint function sets give the same value on any planar #CSP instance, we apply a novel form of holographic transformation of Valiant [Valiant, 2008], using the quantum permutation matrix 𝒰 defining the quantum isomorphism. Due to the noncommutativity of 𝒰’s entries, it turns out that this form of holographic transformation is only applicable to planar Holant. To prove the converse, we introduce the quantum automorphism group Qut(ℱ) of a set of constraint functions/tensors ℱ, and characterize the intertwiners of Qut(ℱ) as the signature matrices of planar Holant(ℱ | EQ) quantum gadgets. Then we define a new notion of (projective) connectivity for constraint functions and reduce arity while preserving the quantum automorphism group. Finally, to address the challenges posed by generalizing from 0-1 valued to real-valued constraint functions, we adapt a technique of Lovász [László Lovász, 1967] in the classical setting for isomorphisms of real-weighted graphs to the setting of quantum isomorphisms.
Cite as
Jin-Yi Cai and Ben Young. Planar #CSP Equality Corresponds to Quantum Isomorphism - A Holant Viewpoint. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cai_et_al:LIPIcs.ICALP.2023.33,
author = {Cai, Jin-Yi and Young, Ben},
title = {{Planar #CSP Equality Corresponds to Quantum Isomorphism - A Holant Viewpoint}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {33:1--33:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.33},
URN = {urn:nbn:de:0030-drops-180851},
doi = {10.4230/LIPIcs.ICALP.2023.33},
annote = {Keywords: #CSP, Quantum isomorphism, Holant, Gadget, Intertwiners, Planar graphs}
}
Document
Track A: Algorithms, Complexity and Games
On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete k-Center for Small k
Abstract
We study the time complexity of the discrete k-center problem and related (exact) geometric set cover problems when k or the size of the cover is small. We obtain a plethora of new results:
- We give the first subquadratic algorithm for rectilinear discrete 3-center in 2D, running in Õ(n^{3/2}) time.
- We prove a lower bound of Ω(n^{4/3-δ}) for rectilinear discrete 3-center in 4D, for any constant δ > 0, under a standard hypothesis about triangle detection in sparse graphs.
- Given n points and n weighted axis-aligned unit squares in 2D, we give the first subquadratic algorithm for finding a minimum-weight cover of the points by 3 unit squares, running in Õ(n^{8/5}) time. We also prove a lower bound of Ω(n^{3/2-δ}) for the same problem in 2D, under the well-known APSP Hypothesis. For arbitrary axis-aligned rectangles in 2D, our upper bound is Õ(n^{7/4}).
- We prove a lower bound of Ω(n^{2-δ}) for Euclidean discrete 2-center in 13D, under the Hyperclique Hypothesis. This lower bound nearly matches the straightforward upper bound of Õ(n^ω), if the matrix multiplication exponent ω is equal to 2.
- We similarly prove an Ω(n^{k-δ}) lower bound for Euclidean discrete k-center in O(k) dimensions for any constant k ≥ 3, under the Hyperclique Hypothesis. This lower bound again nearly matches known upper bounds if ω = 2.
- We also prove an Ω(n^{2-δ}) lower bound for the problem of finding 2 boxes to cover the largest number of points, given n points and n boxes in 12D . This matches the straightforward near-quadratic upper bound.
Cite as
Timothy M. Chan, Qizheng He, and Yuancheng Yu. On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete k-Center for Small k. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 34:1-34:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chan_et_al:LIPIcs.ICALP.2023.34,
author = {Chan, Timothy M. and He, Qizheng and Yu, Yuancheng},
title = {{On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete k-Center for Small k}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {34:1--34:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.34},
URN = {urn:nbn:de:0030-drops-180868},
doi = {10.4230/LIPIcs.ICALP.2023.34},
annote = {Keywords: Geometric set cover, discrete k-center, conditional lower bounds}
}
Document
Track A: Algorithms, Complexity and Games
Ortho-Radial Drawing in Near-Linear Time
Abstract
An orthogonal drawing is an embedding of a plane graph into a grid. In a seminal work of Tamassia (SIAM Journal on Computing 1987), a simple combinatorial characterization of angle assignments that can be realized as bend-free orthogonal drawings was established, thereby allowing an orthogonal drawing to be described combinatorially by listing the angles of all corners. The characterization reduces the need to consider certain geometric aspects, such as edge lengths and vertex coordinates, and simplifies the task of graph drawing algorithm design.
Barth, Niedermann, Rutter, and Wolf (SoCG 2017) established an analogous combinatorial characterization for ortho-radial drawings, which are a generalization of orthogonal drawings to cylindrical grids. The proof of the characterization is existential and does not result in an efficient algorithm. Niedermann, Rutter, and Wolf (SoCG 2019) later addressed this issue by developing quadratic-time algorithms for both testing the realizability of a given angle assignment as an ortho-radial drawing without bends and constructing such a drawing.
In this paper, we improve the time complexity of these tasks to near-linear time. We establish a new characterization for ortho-radial drawings based on the concept of a good sequence. Using the new characterization, we design a simple greedy algorithm for constructing ortho-radial drawings.
Cite as
Yi-Jun Chang. Ortho-Radial Drawing in Near-Linear Time. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chang:LIPIcs.ICALP.2023.35,
author = {Chang, Yi-Jun},
title = {{Ortho-Radial Drawing in Near-Linear Time}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {35:1--35:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.35},
URN = {urn:nbn:de:0030-drops-180879},
doi = {10.4230/LIPIcs.ICALP.2023.35},
annote = {Keywords: Graph drawing, ortho-radial drawing, topology-shape-metric framework}
}
Document
Track A: Algorithms, Complexity and Games
Approximation Algorithms for Network Design in Non-Uniform Fault Models
Abstract
Classical network design models, such as the Survivable Network Design problem (SNDP), are (partly) motivated by robustness to faults under the assumption that any subset of edges upto a specific number can fail. We consider non-uniform fault models where the subset of edges that fail can be specified in different ways. Our primary interest is in the flexible graph connectivity model [Adjiashvili, 2013; Adjiashvili et al., 2020; Adjiashvili et al., 2022; Boyd et al., 2023], in which the edge set is partitioned into safe and unsafe edges. Given parameters p,q ≥ 1, the goal is to find a cheap subgraph that remains p-connected even after the failure of q unsafe edges. We also discuss the bulk-robust model [Adjiashvili et al., 2015; Adjiashvili, 2015] and the relative survivable network design model [Dinitz et al., 2022]. While SNDP admits a 2-approximation [K. Jain, 2001], the approximability of problems in these more complex models is much less understood even in special cases. We make two contributions.
Our first set of results are in the flexible graph connectivity model. Motivated by a conjecture that a constant factor approximation is feasible when p and q are fixed, we consider two special cases. For the s-t case we obtain an approximation ratio that depends only on p,q whenever p+q > pq/2 which includes (p,2) and (2,q) for all p,q ≥ 1. For the global connectivity case we obtain an O(q) approximation for (2,q), and an O(p) approximation for (p,2) and (p,3) for any p ≥ 1, and for (p,4) when p is even. These are based on an augmentation framework and decomposing the families of cuts that need to be covered into a small number of uncrossable families.
Our second result is a poly-logarithmic approximation for a generalization of the bulk-robust model when the "width" of the given instance (the maximum number of edges that can fail in any particular scenario) is fixed. Via this, we derive corresponding approximations for the flexible graph connectivity model and the relative survivable network design model. We utilize a recent framework due to Chen et al. [Chen et al., 2022] that was designed for handling group connectivity.
Cite as
Chandra Chekuri and Rhea Jain. Approximation Algorithms for Network Design in Non-Uniform Fault Models. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chekuri_et_al:LIPIcs.ICALP.2023.36,
author = {Chekuri, Chandra and Jain, Rhea},
title = {{Approximation Algorithms for Network Design in Non-Uniform Fault Models}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {36:1--36:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.36},
URN = {urn:nbn:de:0030-drops-180885},
doi = {10.4230/LIPIcs.ICALP.2023.36},
annote = {Keywords: non-uniform faults, network design, approximation algorithm}
}
Document
Track A: Algorithms, Complexity and Games
Sublinear Algorithms and Lower Bounds for Estimating MST and TSP Cost in General Metrics
Abstract
We consider the design of sublinear space and query complexity algorithms for estimating the cost of a minimum spanning tree (MST) and the cost of a minimum traveling salesman (TSP) tour in a metric on n points. We start by exploring this estimation task in the regime of o(n) space, when the input is presented as a stream of all binom(n,2) entries of the metric in an arbitrary order (a metric stream). For any α ≥ 2, we show that both MST and TSP cost can be α-approximated using Õ(n/α) space, and moreover, Ω(n/α²) space is necessary for this task. We further show that even if the streaming algorithm is allowed p passes over a metric stream, it still requires Ω̃(√{n/α p²}) space.
We next consider the well-studied semi-streaming regime. In this regime, it is straightforward to compute MST cost exactly even in the case where the input stream only contains the edges of a weighted graph that induce the underlying metric (a graph stream), and the main challenging problem is to estimate TSP cost to within a factor that is strictly better than 2. We show that in graph streams, for any ε > 0, any one-pass (2-ε)-approximation of TSP cost requires Ω(ε² n²) space. On the other hand, we show that there is an Õ(n) space two-pass algorithm that approximates the TSP cost to within a factor of 1.96.
Finally, we consider the query complexity of estimating metric TSP cost to within a factor that is strictly better than 2 when the algorithm is given access to an n × n matrix that specifies pairwise distances between n points. The problem of MST cost estimation in this model is well-understood and a (1+ε)-approximation is achievable by Õ(n/ε^{O(1)}) queries. However, for estimating TSP cost, it is known that an analogous result requires Ω(n²) queries even for (1,2)-TSP, and for general metrics, no algorithm that achieves a better than 2-approximation with o(n²) queries is known. We make progress on this task by designing an algorithm that performs Õ(n^{1.5}) distance queries and achieves a strictly better than 2-approximation when either the metric is known to contain a spanning tree supported on weight-1 edges or the algorithm is given access to a minimum spanning tree of the graph. Prior to our work, such results were only known for the special cases of graphic TSP and (1,2)-TSP.
In terms of techniques, our algorithms for metric TSP cost estimation in both streaming and query settings rely on estimating the cover advantage which intuitively measures the cost needed to turn an MST into an Eulerian graph. One of our main algorithmic contributions is to show that this quantity can be meaningfully estimated by a sublinear number of queries in the query model. On one hand, the fact that a metric stream reveals pairwise distances for all pairs of vertices provably helps algorithmically. On the other hand, it also seems to render useless techniques for proving space lower bounds via reductions from well-known hard communication problems. Our main technical contribution in lower bounds is to identify and characterize the communication complexity of new problems that can serve as canonical starting point for proving metric stream lower bounds.
Cite as
Yu Chen, Sanjeev Khanna, and Zihan Tan. Sublinear Algorithms and Lower Bounds for Estimating MST and TSP Cost in General Metrics. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.37,
author = {Chen, Yu and Khanna, Sanjeev and Tan, Zihan},
title = {{Sublinear Algorithms and Lower Bounds for Estimating MST and TSP Cost in General Metrics}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {37:1--37:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.37},
URN = {urn:nbn:de:0030-drops-180892},
doi = {10.4230/LIPIcs.ICALP.2023.37},
annote = {Keywords: Minimum spanning tree, travelling salesman problem, streaming algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints
Abstract
Lasso and Ridge are important minimization problems in machine learning and statistics. They are versions of linear regression with squared loss where the vector θ ∈ ℝ^d of coefficients is constrained in either 𝓁₁-norm (for Lasso) or in 𝓁₂-norm (for Ridge). We study the complexity of quantum algorithms for finding ε-minimizers for these minimization problems. We show that for Lasso we can get a quadratic quantum speedup in terms of d by speeding up the cost-per-iteration of the Frank-Wolfe algorithm, while for Ridge the best quantum algorithms are linear in d, as are the best classical algorithms. As a byproduct of our quantum lower bound for Lasso, we also prove the first classical lower bound for Lasso that is tight up to polylog-factors.
Cite as
Yanlin Chen and Ronald de Wolf. Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.38,
author = {Chen, Yanlin and de Wolf, Ronald},
title = {{Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {38:1--38:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.38},
URN = {urn:nbn:de:0030-drops-180907},
doi = {10.4230/LIPIcs.ICALP.2023.38},
annote = {Keywords: Quantum algorithms, Regularized linear regression, Lasso, Ridge, Lower bounds}
}
Document
Track A: Algorithms, Complexity and Games
New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs
Abstract
We give the first pseudorandom generators with sub-linear seed length for the following variants of read-once branching programs (roBPs):
1) First, we show there is an explicit PRG of seed length O(log²(n/ε)log(n)) fooling unbounded-width unordered permutation branching programs with a single accept state, where n is the length of the program. Previously, [Lee-Pyne-Vadhan RANDOM 2022] gave a PRG with seed length Ω(n) for this class. For the ordered case, [Hoza-Pyne-Vadhan ITCS 2021] gave a PRG with seed length Õ(log n ⋅ log 1/ε).
2) Second, we show there is an explicit PRG fooling unbounded-width unordered regular branching programs with a single accept state with seed length Õ(√{n ⋅ log 1/ε} + log 1/ε). Previously, no non-trivial PRG (with seed length less than n) was known for this class (even in the ordered setting). For the ordered case, [Bogdanov-Hoza-Prakriya-Pyne CCC 2022] gave an HSG with seed length Õ(log n ⋅ log 1/ε).
3) Third, we show there is an explicit PRG fooling width w adaptive branching programs with seed length O(log n ⋅ log² (nw/ε)). Here, the branching program can choose an input bit to read depending on its current state, while it is guaranteed that on any input x ∈ {0,1}ⁿ, the branching program reads each input bit exactly once. Previously, no PRG with a non-trivial seed length is known for this class.
We remark that there are some functions computable by constant-width adaptive branching programs but not by sub-exponential-width unordered branching programs.
In terms of techniques, we indeed show that the Forbes-Kelly PRG (with the right parameters) from [Forbes-Kelly FOCS 2018] already fools all variants of roBPs above. Our proof adds several new ideas to the original analysis of Forbes-Kelly, and we believe it further demonstrates the versatility of the Forbes-Kelly PRG.
Cite as
Lijie Chen, Xin Lyu, Avishay Tal, and Hongxun Wu. New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.39,
author = {Chen, Lijie and Lyu, Xin and Tal, Avishay and Wu, Hongxun},
title = {{New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {39:1--39:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.39},
URN = {urn:nbn:de:0030-drops-180916},
doi = {10.4230/LIPIcs.ICALP.2023.39},
annote = {Keywords: pseudorandom generators, derandomization, read-once branching programs}
}
Document
Track A: Algorithms, Complexity and Games
Approximate Nearest Neighbor for Polygonal Curves Under Fréchet Distance
Abstract
We propose κ-approximate nearest neighbor (ANN) data structures for n polygonal curves under the Fréchet distance in ℝ^d, where κ ∈ {1+ε,3+ε} and d ≥ 2. We assume that every input curve has at most m vertices, every query curve has at most k vertices, k ≪ m, and k is given for preprocessing. The query times are Õ(k(mn)^{0.5+ε}/ε^d+ k(d/ε)^O(dk)) for (1+ε)-ANN and Õ(k(mn)^{0.5+ε}/ε^d) for (3+ε)-ANN. The space and expected preprocessing time are Õ(k(mnd^d/ε^d)^O(k+1/ε²)) in both cases. In two and three dimensions, we improve the query times to O(1/ε)^O(k) ⋅ Õ(k) for (1+ε)-ANN and Õ(k) for (3+ε)-ANN. The space and expected preprocessing time improve to O(mn/ε)^O(k) ⋅ Õ(k) in both cases. For ease of presentation, we treat factors in our bounds that depend purely on d as O(1). The hidden polylog factors in the big-Õ notation have powers dependent on d.
Cite as
Siu-Wing Cheng and Haoqiang Huang. Approximate Nearest Neighbor for Polygonal Curves Under Fréchet Distance. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cheng_et_al:LIPIcs.ICALP.2023.40,
author = {Cheng, Siu-Wing and Huang, Haoqiang},
title = {{Approximate Nearest Neighbor for Polygonal Curves Under Fr\'{e}chet Distance}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {40:1--40:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.40},
URN = {urn:nbn:de:0030-drops-180929},
doi = {10.4230/LIPIcs.ICALP.2023.40},
annote = {Keywords: Polygonal curves, Fr\'{e}chet distance, approximate nearest neighbor}
}
Document
Track A: Algorithms, Complexity and Games
Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes
Abstract
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li [Kuan Cheng et al., 2021] showed the existence of asymptotically good linear insdel codes that can correct arbitrarily close to 1 fraction of errors over some constant size alphabet, or achieve rate arbitrarily close to 1/2 even over the binary alphabet. As shown in [Kuan Cheng et al., 2021], these bounds are also the best possible. However, known explicit constructions in [Kuan Cheng et al., 2021], and subsequent improved constructions by Con, Shpilka, and Tamo [Con et al., 2022] all fall short of meeting these bounds. Over any constant size alphabet, they can only achieve rate < 1/8 or correct < 1/4 fraction of errors; over the binary alphabet, they can only achieve rate < 1/1216 or correct < 1/54 fraction of errors. Apparently, previous techniques face inherent barriers to achieve rate better than 1/4 or correct more than 1/2 fraction of errors.
In this work we give new constructions of such codes that meet these bounds, namely, asymptotically good linear insdel codes that can correct arbitrarily close to 1 fraction of errors over some constant size alphabet, and binary asymptotically good linear insdel codes that can achieve rate arbitrarily close to 1/2. All our constructions are efficiently encodable and decodable. Our constructions are based on a novel approach of code concatenation, which embeds the index information implicitly into codewords. This significantly differs from previous techniques and may be of independent interest. Finally, we also prove the existence of linear concatenated insdel codes with parameters that match random linear codes, and propose a conjecture about linear insdel codes.
Cite as
Kuan Cheng, Zhengzhong Jin, Xin Li, Zhide Wei, and Yu Zheng. Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cheng_et_al:LIPIcs.ICALP.2023.41,
author = {Cheng, Kuan and Jin, Zhengzhong and Li, Xin and Wei, Zhide and Zheng, Yu},
title = {{Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {41:1--41:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.41},
URN = {urn:nbn:de:0030-drops-180931},
doi = {10.4230/LIPIcs.ICALP.2023.41},
annote = {Keywords: Error correcting code, Edit distance, Pseudorandomness, Derandomization}
}
Document
Track A: Algorithms, Complexity and Games
Online Learning and Disambiguations of Partial Concept Classes
Abstract
In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a partial concept class is always inherited from the learnability of some "extension" of it to a total concept class.
They showed this is not the case for PAC learning but left the problem open for the stronger notion of online learnability.
We resolve this problem by constructing a class of partial concepts that is online learnable, but no extension of it to a class of total concepts is online learnable (or even PAC learnable).
Cite as
Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini. Online Learning and Disambiguations of Partial Concept Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cheung_et_al:LIPIcs.ICALP.2023.42,
author = {Cheung, Tsun-Ming and Hatami, Hamed and Hatami, Pooya and Hosseini, Kaave},
title = {{Online Learning and Disambiguations of Partial Concept Classes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {42:1--42:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.42},
URN = {urn:nbn:de:0030-drops-180946},
doi = {10.4230/LIPIcs.ICALP.2023.42},
annote = {Keywords: Online learning, Littlestone dimension, VC dimension, partial concept class, clique vs independent set, Alon-Saks-Seymour conjecture, Standard Optimal Algorithm, PAC learning}
}
Document
Track A: Algorithms, Complexity and Games
A General Framework for Learning-Augmented Online Allocation
Abstract
Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of fundamental problems such as the Santa Claus problem (maximizing minimum utility), Nash welfare maximization (maximizing geometric mean of utilities), makespan minimization (minimizing maximum cost), minimization of 𝓁_p-norms, and so on. We focus on divisible items (i.e., fractional allocations) in this paper. Even for divisible items, these problems are characterized by strong super-constant lower bounds in the classical worst-case online model.
In this paper, we study online allocations in the learning-augmented setting, i.e., where the algorithm has access to some additional (machine-learned) information about the problem instance. We introduce a general algorithmic framework for learning-augmented online allocation that produces nearly optimal solutions for this broad range of maximization and minimization objectives using only a single learned parameter for every agent. As corollaries of our general framework, we improve prior results of Lattanzi et al. (SODA 2020) and Li and Xian (ICML 2021) for learning-augmented makespan minimization, and obtain the first learning-augmented nearly-optimal algorithms for the other objectives such as Santa Claus, Nash welfare, 𝓁_p-minimization, etc. We also give tight bounds on the resilience of our algorithms to errors in the learned parameters, and study the learnability of these parameters.
Cite as
Ilan Reuven Cohen and Debmalya Panigrahi. A General Framework for Learning-Augmented Online Allocation. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cohen_et_al:LIPIcs.ICALP.2023.43,
author = {Cohen, Ilan Reuven and Panigrahi, Debmalya},
title = {{A General Framework for Learning-Augmented Online Allocation}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {43:1--43:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.43},
URN = {urn:nbn:de:0030-drops-180952},
doi = {10.4230/LIPIcs.ICALP.2023.43},
annote = {Keywords: Algorithms with predictions, Scheduling algorithms, Online algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Sample-Based Distance-Approximation for Subsequence-Freeness
Abstract
In this work, we study the problem of approximating the distance to subsequence-freeness in the sample-based distribution-free model. For a given subsequence (word) w = w_1 … w_k, a sequence (text) T = t_1 … t_n is said to contain w if there exist indices 1 ≤ i_1 < … < i_k ≤ n such that t_{i_{j}} = w_j for every 1 ≤ j ≤ k. Otherwise, T is w-free. Ron and Rosin (ACM TOCT 2022) showed that the number of samples both necessary and sufficient for one-sided error testing of subsequence-freeness in the sample-based distribution-free model is Θ(k/ε).
Denoting by Δ(T,w,p) the distance of T to w-freeness under a distribution p:[n] → [0,1], we are interested in obtaining an estimate Δ̂, such that |Δ̂ - Δ(T,w,p)| ≤ δ with probability at least 2/3, for a given distance parameter δ. Our main result is an algorithm whose sample complexity is Õ(k²/δ²). We first present an algorithm that works when the underlying distribution p is uniform, and then show how it can be modified to work for any (unknown) distribution p. We also show that a quadratic dependence on 1/δ is necessary.
Cite as
Omer Cohen Sidon and Dana Ron. Sample-Based Distance-Approximation for Subsequence-Freeness. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cohensidon_et_al:LIPIcs.ICALP.2023.44,
author = {Cohen Sidon, Omer and Ron, Dana},
title = {{Sample-Based Distance-Approximation for Subsequence-Freeness}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {44:1--44:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.44},
URN = {urn:nbn:de:0030-drops-180964},
doi = {10.4230/LIPIcs.ICALP.2023.44},
annote = {Keywords: Property Testing, Distance Approximation}
}
Document
Track A: Algorithms, Complexity and Games
New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling
Abstract
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable us to view an instance of interval scheduling on many jobs as a union of multiple interval scheduling instances, each containing only a few jobs. Instantiating these techniques in dynamic and local settings of computation leads to several new results.
For (1+ε)-approximation of job scheduling of n jobs on a single machine, we develop a fully dynamic algorithm with O((log n)/ε) update and O(log n) query worst-case time. Further, we design a local computation algorithm that uses only O((log N)/ε) queries when all jobs are length at least 1 and have starting/ending times within [0,N]. Our techniques are also applicable in a setting where jobs have rewards/weights. For this case we design a fully dynamic deterministic algorithm whose worst-case update and query time are poly(log n,1/ε). Equivalently, this is the first algorithm that maintains a (1+ε)-approximation of the maximum independent set of a collection of weighted intervals in poly(log n,1/ε) time updates/queries. This is an exponential improvement in 1/ε over the running time of a randomized algorithm of Henzinger, Neumann, and Wiese [SoCG, 2020], while also removing all dependence on the values of the jobs' starting/ending times and rewards, as well as removing the need for any randomness.
We also extend our approaches for interval scheduling on a single machine to examine the setting with M machines.
Cite as
Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld. New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{compton_et_al:LIPIcs.ICALP.2023.45,
author = {Compton, Spencer and Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt},
title = {{New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {45:1--45:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.45},
URN = {urn:nbn:de:0030-drops-180978},
doi = {10.4230/LIPIcs.ICALP.2023.45},
annote = {Keywords: interval scheduling, dynamic algorithms, local computation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Optimal (Degree+1)-Coloring in Congested Clique
Abstract
We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node u of degree d(u) is assigned a palette of d(u)+1 colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing.
In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.
Cite as
Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. Optimal (Degree+1)-Coloring in Congested Clique. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{coy_et_al:LIPIcs.ICALP.2023.46,
author = {Coy, Sam and Czumaj, Artur and Davies, Peter and Mishra, Gopinath},
title = {{Optimal (Degree+1)-Coloring in Congested Clique}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {46:1--46:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.46},
URN = {urn:nbn:de:0030-drops-180987},
doi = {10.4230/LIPIcs.ICALP.2023.46},
annote = {Keywords: Distributed computing, graph coloring, parallel computing}
}
Document
Track A: Algorithms, Complexity and Games
Incremental Maximization via Continuization
Abstract
We consider the problem of finding an incremental solution to a cardinality-constrained maximization problem that not only captures the solution for a fixed cardinality, but also describes how to gradually grow the solution as the cardinality bound increases. The goal is to find an incremental solution that guarantees a good competitive ratio against the optimum solution for all cardinalities simultaneously. The central challenge is to characterize maximization problems where this is possible, and to determine the best-possible competitive ratio that can be attained. A lower bound of 2.18 and an upper bound of φ + 1 ≈ 2.618 are known on the competitive ratio for monotone and accountable objectives [Bernstein et al., Math. Prog., 2022], which capture a wide range of maximization problems. We introduce a continuization technique and identify an optimal incremental algorithm that provides strong evidence that φ + 1 is the best-possible competitive ratio. Using this continuization, we obtain an improved lower bound of 2.246 by studying a particular recurrence relation whose characteristic polynomial has complex roots exactly beyond the lower bound. Based on the optimal continuous algorithm combined with a scaling approach, we also provide a 1.772-competitive randomized algorithm. We complement this by a randomized lower bound of 1.447 via Yao’s principle.
Cite as
Yann Disser, Max Klimm, Kevin Schewior, and David Weckbecker. Incremental Maximization via Continuization. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{disser_et_al:LIPIcs.ICALP.2023.47,
author = {Disser, Yann and Klimm, Max and Schewior, Kevin and Weckbecker, David},
title = {{Incremental Maximization via Continuization}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {47:1--47:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.47},
URN = {urn:nbn:de:0030-drops-180992},
doi = {10.4230/LIPIcs.ICALP.2023.47},
annote = {Keywords: incremental optimization, competitive analysis, robust matching, submodular function}
}
Document
Track A: Algorithms, Complexity and Games
Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach
Abstract
We investigate local computation algorithms (LCA) for two-coloring of k-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lovász Local Lemma of the form 2^(1-αk) (Δ+1) e < 1, where Δ is the bound on the maximum edge degree. The main question which arises here is for how large α there exists an LCA that is able to properly color such hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical sequential procedure of Beck from 1991 with Moser and Tardos' Resample yields polylogarithmic LCA that works for α up to 1/4. Then, we present an improved procedure that solves wider range of instances by allowing α up to 1/3.
Cite as
Andrzej Dorobisz and Jakub Kozik. Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 48:1-48:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{dorobisz_et_al:LIPIcs.ICALP.2023.48,
author = {Dorobisz, Andrzej and Kozik, Jakub},
title = {{Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {48:1--48:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.48},
URN = {urn:nbn:de:0030-drops-181002},
doi = {10.4230/LIPIcs.ICALP.2023.48},
annote = {Keywords: Local Computation Algorithms, Hypergraph Coloring, Property B}
}
Document
Track A: Algorithms, Complexity and Games
An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets
Abstract
We study the budgeted versions of the well known matching and matroid intersection problems. While both problems admit a polynomial-time approximation scheme (PTAS) [Berger et al. (Math. Programming, 2011), Chekuri, Vondrák and Zenklusen (SODA 2011)], it has been an intriguing open question whether these problems admit a fully PTAS (FPTAS), or even an efficient PTAS (EPTAS).
In this paper we answer the second part of this question affirmatively, by presenting an EPTAS for budgeted matching and budgeted matroid intersection. A main component of our scheme is a construction of representative sets for desired solutions, whose cardinality depends only on ε, the accuracy parameter. Thus, enumerating over solutions within a representative set leads to an EPTAS. This crucially distinguishes our algorithms from previous approaches, which rely on exhaustive enumeration over the solution set.
Cite as
Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{doronarad_et_al:LIPIcs.ICALP.2023.49,
author = {Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
title = {{An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {49:1--49:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.49},
URN = {urn:nbn:de:0030-drops-181018},
doi = {10.4230/LIPIcs.ICALP.2023.49},
annote = {Keywords: budgeted matching, budgeted matroid intersection, efficient polynomial-time approximation scheme}
}
Document
Track A: Algorithms, Complexity and Games
Connected k-Center and k-Diameter Clustering
Abstract
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graph G on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints.
Our main result is an O(1)-approximation algorithm for the disjoint connected k-center and k-diameter problem for Euclidean spaces of low dimension (constant d) and for metrics with constant doubling dimension. For general metrics, we get an O(log²k)-approximation. Our algorithms work by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering.
We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.
Cite as
Lukas Drexler, Jan Eube, Kelin Luo, Heiko Röglin, Melanie Schmidt, and Julian Wargalla. Connected k-Center and k-Diameter Clustering. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{drexler_et_al:LIPIcs.ICALP.2023.50,
author = {Drexler, Lukas and Eube, Jan and Luo, Kelin and R\"{o}glin, Heiko and Schmidt, Melanie and Wargalla, Julian},
title = {{Connected k-Center and k-Diameter Clustering}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {50:1--50:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.50},
URN = {urn:nbn:de:0030-drops-181024},
doi = {10.4230/LIPIcs.ICALP.2023.50},
annote = {Keywords: Approximation algorithms, Clustering, Connectivity constraints}
}
Document
Track A: Algorithms, Complexity and Games
On Sparsification of Stochastic Packing Problems
Abstract
Motivated by recent progress on stochastic matching with few queries, we embark on a systematic study of the sparsification of stochastic packing problems more generally. Specifically, we consider packing problems where elements are independently active with a given probability p, and ask whether one can (non-adaptively) compute a "sparse" set of elements guaranteed to contain an approximately optimal solution to the realized (active) subproblem. We seek structural and algorithmic results of broad applicability to such problems. Our focus is on computing sparse sets containing on the order of d feasible solutions to the packing problem, where d is linear or at most polynomial in 1/p. Crucially, we require d to be independent of the number of elements, or any parameter related to the "size" of the packing problem. We refer to d as the "degree" of the sparsifier, as is consistent with graph theoretic degree in the special case of matching.
First, we exhibit a generic sparsifier of degree 1/p based on contention resolution. This sparsifier’s approximation ratio matches the best contention resolution scheme (CRS) for any packing problem for additive objectives, and approximately matches the best monotone CRS for submodular objectives. Second, we embark on outperforming this generic sparsifier for additive optimization over matroids and their intersections, as well as weighted matching. These improved sparsifiers feature different algorithmic and analytic approaches, and have degree linear in 1/p. In the case of a single matroid, our sparsifier tends to the optimal solution. In the case of weighted matching, we combine our contention-resolution-based sparsifier with technical approaches of prior work to improve the state of the art ratio from 0.501 to 0.536. Third, we examine packing problems with submodular objectives. We show that even the simplest such problems do not admit sparsifiers approaching optimality. We then outperform our generic sparsifier for some special cases with submodular objectives.
Cite as
Shaddin Dughmi, Yusuf Hakan Kalayci, and Neel Patel. On Sparsification of Stochastic Packing Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{dughmi_et_al:LIPIcs.ICALP.2023.51,
author = {Dughmi, Shaddin and Kalayci, Yusuf Hakan and Patel, Neel},
title = {{On Sparsification of Stochastic Packing Problems}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {51:1--51:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.51},
URN = {urn:nbn:de:0030-drops-181036},
doi = {10.4230/LIPIcs.ICALP.2023.51},
annote = {Keywords: Stochastic packing, sparsification, matroid}
}
Document
Track A: Algorithms, Complexity and Games
Triangle Counting with Local Edge Differential Privacy
Abstract
Many deployments of differential privacy in industry are in the local model, where each party releases its private information via a differentially private randomizer. We study triangle counting in the noninteractive and interactive local model with edge differential privacy (that, intuitively, requires that the outputs of the algorithm on graphs that differ in one edge be indistinguishable). In this model, each party’s local view consists of the adjacency list of one vertex.
In the noninteractive model, we prove that additive Ω(n²) error is necessary, where n is the number of nodes. This lower bound is our main technical contribution. It uses a reconstruction attack with a new class of linear queries and a novel mix-and-match strategy of running the local randomizers with different completions of their adjacency lists. It matches the additive error of the algorithm based on Randomized Response, proposed by Imola, Murakami and Chaudhuri (USENIX2021) and analyzed by Imola, Murakami and Chaudhuri (CCS2022) for constant ε. We use a different postprocessing of Randomized Response and provide tight bounds on the variance of the resulting algorithm.
In the interactive setting, we prove a lower bound of Ω(n^{3/2}) on the additive error. Previously, no hardness results were known for interactive, edge-private algorithms in the local model, except for those that follow trivially from the results for the central model. Our work significantly improves on the state of the art in differentially private graph analysis in the local model.
Cite as
Talya Eden, Quanquan C. Liu, Sofya Raskhodnikova, and Adam Smith. Triangle Counting with Local Edge Differential Privacy. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 52:1-52:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{eden_et_al:LIPIcs.ICALP.2023.52,
author = {Eden, Talya and Liu, Quanquan C. and Raskhodnikova, Sofya and Smith, Adam},
title = {{Triangle Counting with Local Edge Differential Privacy}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {52:1--52:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.52},
URN = {urn:nbn:de:0030-drops-181048},
doi = {10.4230/LIPIcs.ICALP.2023.52},
annote = {Keywords: local differential privacy, reconstruction attacks, lower bounds, triangle counting}
}
Document
Track A: Algorithms, Complexity and Games
Protecting Single-Hop Radio Networks from Message Drops
Abstract
Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the n participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic message drops (i.e., erasures), where in every round, the message received by each party is erased (replaced by ⊥) with some small constant probability, independently.
Our main result is a constant rate coding scheme, allowing one to run protocols designed to work over the (noiseless) SHRN model over the SHRN model with erasures. Our scheme converts any protocol Π of length at most exponential in n over the SHRN model to a protocol Π' that is resilient to constant fraction of erasures and has length linear in the length of Π.
We mention that for the special case where the protocol Π is non-adaptive, i.e., the order of communication is fixed in advance, such a scheme was known. Nevertheless, adaptivity is widely used and is known to hugely boost the power of wireless channels, which makes handling the general case of adaptive protocols Π both important and more challenging. Indeed, to the best of our knowledge, our result is the first constant rate scheme that converts adaptive protocols to noise resilient ones in any multi-party model.
Cite as
Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Protecting Single-Hop Radio Networks from Message Drops. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{efremenko_et_al:LIPIcs.ICALP.2023.53,
author = {Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R.},
title = {{Protecting Single-Hop Radio Networks from Message Drops}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {53:1--53:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.53},
URN = {urn:nbn:de:0030-drops-181059},
doi = {10.4230/LIPIcs.ICALP.2023.53},
annote = {Keywords: Radio Networks, Interactive Coding, Error Correcting Codes}
}
Document
Track A: Algorithms, Complexity and Games
On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n)
Abstract
We study the single-site Glauber dynamics for the fugacity λ, Hard-Core model on the random graph G(n, d/n). We show that for the typical instances of the random graph G(n,d/n) and for fugacity λ < {d^d} / {(d-1)^(d+1)}, the mixing time of Glauber dynamics is n^{1 + O(1/log log n)}.
Our result improves on the recent elegant algorithm in [Bezáková, Galanis, Goldberg and Štefankovič; ICALP'22]. The algorithm there is an MCMC-based sampling algorithm, but it is not the Glauber dynamics. Our algorithm here is simpler, as we use the classic Glauber dynamics. Furthermore, the bounds on mixing time we prove are smaller than those in Bezáková et al. paper, hence our algorithm is also faster.
The main challenge in our proof is handling vertices with unbounded degrees. We provide stronger results with regard the spectral independence via branching values and show that the our Gibbs distributions satisfy the approximate tensorisation of the entropy. We conjecture that the bounds we have here are optimal for G(n,d/n).
As corollary of our analysis for the Hard-Core model, we also get bounds on the mixing time of the Glauber dynamics for the Monomer-Dimer model on G(n,d/n). The bounds we get for this model are slightly better than those we have for the Hard-Core model
Cite as
Charilaos Efthymiou and Weiming Feng. On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{efthymiou_et_al:LIPIcs.ICALP.2023.54,
author = {Efthymiou, Charilaos and Feng, Weiming},
title = {{On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n)}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {54:1--54:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.54},
URN = {urn:nbn:de:0030-drops-181064},
doi = {10.4230/LIPIcs.ICALP.2023.54},
annote = {Keywords: spin-system, spin-glass, sparse random (hyper)graph, approximate sampling, efficient algorithm}
}
Document
Track A: Algorithms, Complexity and Games
Broadcasting with Random Matrices
Abstract
Motivated by the theory of spin-glasses in physics, we study the so-called reconstruction problem on the tree, and on the sparse random graph G(n,d/n). Both cases reduce naturally to analysing broadcasting models, where each edge has its own broadcasting matrix, and this matrix is drawn independently from a predefined distribution.
We establish the reconstruction threshold for the cases where the broadcasting matrices give rise to symmetric, 2-spin Gibbs distributions. This threshold seems to be a natural extension of the well-known Kesten-Stigum bound that manifests in the classic version of the reconstruction problem. Our results determine, as a special case, the reconstruction threshold for the prominent Edwards–Anderson model of spin-glasses, on the tree.
Also, we extend our analysis to the setting of the Galton-Watson random tree, and the (sparse) random graph G(n,d/n), where we establish the corresponding thresholds. Interestingly, for the Edwards–Anderson model on the random graph, we show that the replica symmetry breaking phase transition, established by Guerra and and Toninelli in [Guerra and Toninelli, 2004], coincides with the reconstruction threshold.
Compared to classical Gibbs distributions, spin-glasses have several unique features. In that respect, their study calls for new ideas, e.g. we introduce novel estimators for the reconstruction problem. The main technical challenge in the analysis of such systems, is the presence of (too) many levels of randomness, which we manage to circumvent by utilising recently proposed tools coming from the analysis of Markov chains.
Cite as
Charilaos Efthymiou and Kostas Zampetakis. Broadcasting with Random Matrices. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 55:1-55:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{efthymiou_et_al:LIPIcs.ICALP.2023.55,
author = {Efthymiou, Charilaos and Zampetakis, Kostas},
title = {{Broadcasting with Random Matrices}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {55:1--55:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.55},
URN = {urn:nbn:de:0030-drops-181070},
doi = {10.4230/LIPIcs.ICALP.2023.55},
annote = {Keywords: spin-system, spin-glass, sparse random graph, reconstruction, phase transitions}
}
Document
Track A: Algorithms, Complexity and Games
Improved Mixing for the Convex Polygon Triangulation Flip Walk
Abstract
We prove that the well-studied triangulation flip walk on a convex point set mixes in time O(n³ log³ n), the first progress since McShine and Tetali’s O(n⁵ log n) bound in 1997. In the process we give lower and upper bounds of respectively Ω(1/(√n log n)) and O(1/√n) - asymptotically tight up to an O(log n) factor - for the expansion of the associahedron graph K_n. The upper bound recovers Molloy, Reed, and Steiger’s Ω(n^(3/2)) bound on the mixing time of the walk. To obtain these results, we introduce a framework consisting of a set of sufficient conditions under which a given Markov chain mixes rapidly. This framework is a purely combinatorial analogue that in some circumstances gives better results than the projection-restriction technique of Jerrum, Son, Tetali, and Vigoda. In particular, in addition to the result for triangulations, we show quasipolynomial mixing for the k-angulation flip walk on a convex point set, for fixed k ≥ 4.
Cite as
David Eppstein and Daniel Frishberg. Improved Mixing for the Convex Polygon Triangulation Flip Walk. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 56:1-56:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{eppstein_et_al:LIPIcs.ICALP.2023.56,
author = {Eppstein, David and Frishberg, Daniel},
title = {{Improved Mixing for the Convex Polygon Triangulation Flip Walk}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {56:1--56:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.56},
URN = {urn:nbn:de:0030-drops-181081},
doi = {10.4230/LIPIcs.ICALP.2023.56},
annote = {Keywords: associahedron, mixing time, mcmc, Markov chains, triangulations, quadrangulations, k-angulations, multicommodity flow, projection-restriction}
}
Document
Track A: Algorithms, Complexity and Games
Optimal Adjacency Labels for Subgraphs of Cartesian Products
Abstract
For any hereditary graph class ℱ, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in ℱ. As a consequence, we show that, if ℱ admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then the classes of subgraphs and induced subgraphs of Cartesian products of graphs in ℱ do too. Our proof uses ideas from randomized communication complexity and hashing, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020].
Cite as
Louis Esperet, Nathaniel Harms, and Viktor Zamaraev. Optimal Adjacency Labels for Subgraphs of Cartesian Products. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 57:1-57:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{esperet_et_al:LIPIcs.ICALP.2023.57,
author = {Esperet, Louis and Harms, Nathaniel and Zamaraev, Viktor},
title = {{Optimal Adjacency Labels for Subgraphs of Cartesian Products}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {57:1--57:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.57},
URN = {urn:nbn:de:0030-drops-181093},
doi = {10.4230/LIPIcs.ICALP.2023.57},
annote = {Keywords: Adjacency labeling schemes, Cartesian product, Hypercubes}
}
Document
Track A: Algorithms, Complexity and Games
Truthful Matching with Online Items and Offline Agents
Abstract
We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive online in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier up to which the celebrated e/(e-1) competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items.
Cite as
Michal Feldman, Federico Fusco, Simon Mauras, and Rebecca Reiffenhäuser. Truthful Matching with Online Items and Offline Agents. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{feldman_et_al:LIPIcs.ICALP.2023.58,
author = {Feldman, Michal and Fusco, Federico and Mauras, Simon and Reiffenh\"{a}user, Rebecca},
title = {{Truthful Matching with Online Items and Offline Agents}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {58:1--58:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.58},
URN = {urn:nbn:de:0030-drops-181106},
doi = {10.4230/LIPIcs.ICALP.2023.58},
annote = {Keywords: Online matching, Karp-Vazirani-Vazirani, truthfulness}
}
Document
Track A: Algorithms, Complexity and Games
Completely Reachable Automata: A Polynomial Algorithm and Quadratic Upper Bounds
Abstract
A complete deterministic finite (semi)automaton (DFA) with a set of states Q is completely reachable if every non-empty subset of Q can be obtained as the image of the action of some word applied to Q. The concept of completely reachable automata appeared several times, in particular, in connection with synchronizing automata; the class contains the Černý automata and covers a few separately investigated subclasses. The notion was introduced by Bondar and Volkov (2016), who also raised the question about the complexity of deciding if an automaton is completely reachable. We develop a polynomial-time algorithm for this problem, which is based on a new complement-intersecting technique for finding an extending word for a subset of states. The algorithm works in 𝒪(|Σ|⋅ n³) time, where n = |Q| is the number of states and |Σ| is the size of the input alphabet. Finally, we prove a weak Don’s conjecture for this class of automata: a subset of size k is reachable with a word of length smaller than 2n(n-k). This implies a quadratic upper bound in n on the length of the shortest synchronizing words (reset threshold) for the class of completely reachable automata and generalizes earlier upper bounds derived for its subclasses.
Cite as
Robert Ferens and Marek Szykuła. Completely Reachable Automata: A Polynomial Algorithm and Quadratic Upper Bounds. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ferens_et_al:LIPIcs.ICALP.2023.59,
author = {Ferens, Robert and Szyku{\l}a, Marek},
title = {{Completely Reachable Automata: A Polynomial Algorithm and Quadratic Upper Bounds}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {59:1--59:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.59},
URN = {urn:nbn:de:0030-drops-181110},
doi = {10.4230/LIPIcs.ICALP.2023.59},
annote = {Keywords: \v{C}ern\'{y} conjecture, complete reachability, DFA, extending word, reachability, reset threshold, reset word, simple idempotent, synchronizing automaton, synchronizing word}
}
Document
Track A: Algorithms, Complexity and Games
Approximating Long Cycle Above Dirac’s Guarantee
Abstract
Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit "natural" guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on m clauses, there is an assignment that satisfies at least m/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than m/2 + k clauses? Or, if an n-vertex graph has a perfect matching, then its vertex cover is at least n/2. Is there a vertex cover of size at least n/2 + k for some k ≥ 1 and how difficult is it to find such a vertex cover?
The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected n-vertex graph G with minimum degree δ(G) ≤ n/2, the length of the longest cycle L is at least 2δ(G). Thus the "essential" part of finding the longest cycle is in approximating the "offset" k = L - 2δ(G). The main result of this paper is the above-guarantee approximation theorem for k. Informally, the theorem says that approximating the offset k is not harder than approximating the total length L of a cycle. In other words, for any (reasonably well-behaved) function f, a polynomial time algorithm constructing a cycle of length f(L) in an undirected graph with a cycle of length L, yields a polynomial time algorithm constructing a cycle of length 2δ(G)+Ω(f(k)).
Cite as
Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Approximating Long Cycle Above Dirac’s Guarantee. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fomin_et_al:LIPIcs.ICALP.2023.60,
author = {Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
title = {{Approximating Long Cycle Above Dirac’s Guarantee}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {60:1--60:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.60},
URN = {urn:nbn:de:0030-drops-181128},
doi = {10.4230/LIPIcs.ICALP.2023.60},
annote = {Keywords: Longest path, longest cycle, approximation algorithms, above guarantee parameterization, minimum degree, Dirac theorem}
}
Document
Track A: Algorithms, Complexity and Games
Compound Logics for Modification Problems
Abstract
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of sentences, expressing graph modification: the modulator sentence, defining some property of the modified part of the graph, and the target sentence, defining some property of the resulting graph. In our framework, modulator sentences are in counting monadic second-order logic (CMSOL) and have models of bounded treewidth, while target sentences express first-order logic (FOL) properties along with minor-exclusion. Our logic captures problems that are not definable in first-order logic and, moreover, may have instances of unbounded treewidth. Also, it permits the modeling of wide families of problems involving vertex/edge removals, alternative modulator measures (such as elimination distance or G-treewidth), multistage modifications, and various cut problems. Our main result is that, for this compound logic, model-checking can be done in quadratic time. All derived algorithms are constructive and this, as a byproduct, extends the constructibility horizon of the algorithmic applications of the Graph Minors theorem of Robertson and Seymour. The proposed logic can be seen as a general framework to capitalize on the potential of the irrelevant vertex technique. It gives a way to deal with problem instances of unbounded treewidth, for which Courcelle’s theorem does not apply.
Cite as
Fedor V. Fomin, Petr A. Golovach, Ignasi Sau, Giannos Stamoulis, and Dimitrios M. Thilikos. Compound Logics for Modification Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 61:1-61:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fomin_et_al:LIPIcs.ICALP.2023.61,
author = {Fomin, Fedor V. and Golovach, Petr A. and Sau, Ignasi and Stamoulis, Giannos and Thilikos, Dimitrios M.},
title = {{Compound Logics for Modification Problems}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {61:1--61:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.61},
URN = {urn:nbn:de:0030-drops-181137},
doi = {10.4230/LIPIcs.ICALP.2023.61},
annote = {Keywords: Algorithmic meta-theorems, Graph modification problems, Model-checking, Graph minors, First-order logic, Monadic second-order logic, Flat Wall theorem, Irrelevant vertex technique}
}
Document
Track A: Algorithms, Complexity and Games
Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs
Abstract
A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs.
In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.
Cite as
Tobias Friedrich, Andreas Göbel, Maximilian Katzmann, and Leon Schiller. Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{friedrich_et_al:LIPIcs.ICALP.2023.62,
author = {Friedrich, Tobias and G\"{o}bel, Andreas and Katzmann, Maximilian and Schiller, Leon},
title = {{Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {62:1--62:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.62},
URN = {urn:nbn:de:0030-drops-181147},
doi = {10.4230/LIPIcs.ICALP.2023.62},
annote = {Keywords: random graphs, geometry, dimensionality, cliques, clique number, scale-free networks}
}
Document
Track A: Algorithms, Complexity and Games
An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs
Abstract
We present an O(log k)-approximation for both the edge-weighted and node-weighted versions of Directed Steiner Tree in planar graphs where k is the number of terminals. We extend our approach to Multi-Rooted Directed Steiner Tree, in which we get a O(R+log k)-approximation for planar graphs for where R is the number of roots.
Cite as
Zachary Friggstad and Ramin Mousavi. An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{friggstad_et_al:LIPIcs.ICALP.2023.63,
author = {Friggstad, Zachary and Mousavi, Ramin},
title = {{An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {63:1--63:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.63},
URN = {urn:nbn:de:0030-drops-181156},
doi = {10.4230/LIPIcs.ICALP.2023.63},
annote = {Keywords: Directed Steiner tree, Combinatorial optimization, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Parallel Self-Testing of EPR Pairs Under Computational Assumptions
Abstract
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Metger and Vidick, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ε must be poly(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution [Metger et al., 2021] under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
Cite as
Honghao Fu, Daochen Wang, and Qi Zhao. Parallel Self-Testing of EPR Pairs Under Computational Assumptions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fu_et_al:LIPIcs.ICALP.2023.64,
author = {Fu, Honghao and Wang, Daochen and Zhao, Qi},
title = {{Parallel Self-Testing of EPR Pairs Under Computational Assumptions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {64:1--64:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.64},
URN = {urn:nbn:de:0030-drops-181160},
doi = {10.4230/LIPIcs.ICALP.2023.64},
annote = {Keywords: Quantum complexity theory, self-testing, LWE}
}
Document
Track A: Algorithms, Complexity and Games
Matching Augmentation via Simultaneous Contractions
Abstract
We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a 2-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an approximation ratio of 13/8 = 1.625 improving upon an earlier 5/3-approximation. The improvement builds on a new α-approximation preserving reduction for any α ≥ 3/2 from arbitrary MAP instances to well-structured instances that do not contain certain forbidden structures like parallel edges, small separators, and contractible subgraphs. We further introduce, as key ingredients, the technique of repeated simultaneous contractions and provide improved lower bounds for instances that cannot be contracted.
Cite as
Mohit Garg, Felix Hommelsheim, and Nicole Megow. Matching Augmentation via Simultaneous Contractions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{garg_et_al:LIPIcs.ICALP.2023.65,
author = {Garg, Mohit and Hommelsheim, Felix and Megow, Nicole},
title = {{Matching Augmentation via Simultaneous Contractions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {65:1--65:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.65},
URN = {urn:nbn:de:0030-drops-181176},
doi = {10.4230/LIPIcs.ICALP.2023.65},
annote = {Keywords: matching augmentation, approximation algorithms, 2-edge-connectivity}
}
Document
Track A: Algorithms, Complexity and Games
On Differentially Private Counting on Trees
Abstract
We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a combination of multiplicative and additive approximation to the query results. We examine known mechanisms in differential privacy (DP) and prove their optimality, under this measure, in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvements over known ones.
Cite as
Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, and Kewen Wu. On Differentially Private Counting on Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ghazi_et_al:LIPIcs.ICALP.2023.66,
author = {Ghazi, Badih and Kamath, Pritish and Kumar, Ravi and Manurangsi, Pasin and Wu, Kewen},
title = {{On Differentially Private Counting on Trees}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {66:1--66:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.66},
URN = {urn:nbn:de:0030-drops-181186},
doi = {10.4230/LIPIcs.ICALP.2023.66},
annote = {Keywords: Differential Privacy, Algorithms, Trees, Hierarchies}
}
Document
Track A: Algorithms, Complexity and Games
Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More
Abstract
Quantum mechanical effects have enabled the construction of cryptographic primitives that are impossible classically. For example, quantum copy-protection allows for a program to be encoded in a quantum state in such a way that the program can be evaluated, but not copied. Many of these cryptographic primitives are two-party protocols, where one party, Bob, has full quantum computational capabilities, and the other party, Alice, is only required to send random BB84 states to Bob. In this work, we show how such protocols can generically be converted to ones where Alice is fully classical, assuming that Bob cannot efficiently solve the LWE problem. In particular, this means that all communication between (classical) Alice and (quantum) Bob is classical, yet they can still make use of cryptographic primitives that would be impossible if both parties were classical. We apply this conversion procedure to obtain quantum cryptographic protocols with classical communication for unclonable encryption, copy-protection, computing on encrypted data, and verifiable blind delegated computation.
The key technical ingredient for our result is a protocol for classically-instructed parallel remote state preparation of BB84 states. This is a multi-round protocol between (classical) Alice and (quantum polynomial-time) Bob that allows Alice to certify that Bob must have prepared n uniformly random BB84 states (up to a change of basis on his space). While previous approaches could only certify one- or two-qubit states, our protocol allows for the certification of an n-fold tensor product of BB84 states. Furthermore, Alice knows which specific BB84 states Bob has prepared, while Bob himself does not. Hence, the situation at the end of this protocol is (almost) equivalent to one where Alice sent n random BB84 states to Bob. This allows us to replace the step of preparing and sending BB84 states in existing protocols by our remote-state preparation protocol in a generic and modular way.
Cite as
Alexandru Gheorghiu, Tony Metger, and Alexander Poremba. Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 67:1-67:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{gheorghiu_et_al:LIPIcs.ICALP.2023.67,
author = {Gheorghiu, Alexandru and Metger, Tony and Poremba, Alexander},
title = {{Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {67:1--67:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.67},
URN = {urn:nbn:de:0030-drops-181197},
doi = {10.4230/LIPIcs.ICALP.2023.67},
annote = {Keywords: Quantum cryptography, Remote state preparation, Self-testing, Learning with errors, Quantum copy-protection, Unclonable encryption, Quantum verification}
}
Document
Track A: Algorithms, Complexity and Games
Parameterised and Fine-Grained Subgraph Counting, Modulo 2
Abstract
Given a class of graphs ℋ, the problem ⊕Sub(ℋ) is defined as follows. The input is a graph H ∈ ℋ together with an arbitrary graph G. The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H. The goal of this research is to determine for which classes ℋ the problem ⊕Sub(ℋ) is fixed-parameter tractable (FPT), i.e., solvable in time f(|H|)⋅|G|^O(1).
Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕Sub(ℋ) is FPT if and only if the class of allowed patterns ℋ is matching splittable, which means that for some fixed B, every H ∈ ℋ can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices.
Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes ℋ, and (II) all tree pattern classes, i.e., all classes ℋ such that every H ∈ ℋ is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I).
Cite as
Leslie Ann Goldberg and Marc Roth. Parameterised and Fine-Grained Subgraph Counting, Modulo 2. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{goldberg_et_al:LIPIcs.ICALP.2023.68,
author = {Goldberg, Leslie Ann and Roth, Marc},
title = {{Parameterised and Fine-Grained Subgraph Counting, Modulo 2}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {68:1--68:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.68},
URN = {urn:nbn:de:0030-drops-181200},
doi = {10.4230/LIPIcs.ICALP.2023.68},
annote = {Keywords: modular counting, parameterised complexity, fine-grained complexity, subgraph counting}
}
Document
Track A: Algorithms, Complexity and Games
Efficient Data Structures for Incremental Exact and Approximate Maximum Flow
Abstract
We show an (1+ε)-approximation algorithm for maintaining maximum s-t flow under m edge insertions in m^{1/2+o(1)} ε^{-1/2} amortized update time for directed, unweighted graphs. This constitutes the first sublinear dynamic maximum flow algorithm in general sparse graphs with arbitrarily good approximation guarantee.
Furthermore we give an algorithm that maintains an exact maximum s-t flow under m edge insertions in an n-node graph in Õ(n^{5/2}) total update time. For sufficiently dense graphs, this gives to the first exact incremental algorithm with sub-linear amortized update time for maintaining maximum flows.
Cite as
Gramoz Goranci and Monika Henzinger. Efficient Data Structures for Incremental Exact and Approximate Maximum Flow. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{goranci_et_al:LIPIcs.ICALP.2023.69,
author = {Goranci, Gramoz and Henzinger, Monika},
title = {{Efficient Data Structures for Incremental Exact and Approximate Maximum Flow}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {69:1--69:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.69},
URN = {urn:nbn:de:0030-drops-181212},
doi = {10.4230/LIPIcs.ICALP.2023.69},
annote = {Keywords: dynamic graph algorithms, maximum flow, data structures}
}
Document
Track A: Algorithms, Complexity and Games
Low Sample Complexity Participatory Budgeting
Abstract
We study low sample complexity mechanisms in participatory budgeting (PB), where each voter votes for a preferred allocation of funds to various projects, subject to project costs and total spending constraints. We analyse the distortion that PB mechanisms introduce relative to the minimum-social-cost outcome in expectation. The Random Dictator mechanism for this problem obtains a distortion of 2. In a special case where every voter votes for exactly one project, [Fain et al., 2017] obtain a distortion of 4/3. We show that when PB outcomes are determined as any convex combination of the votes of two voters, the distortion is 2. When three uniformly randomly sampled votes are used, we give a PB mechanism that obtains a distortion of at most 1.66, thus breaking the barrier of 2 with the smallest possible sample complexity.
We give a randomized Nash bargaining scheme where two uniformly randomly chosen voters bargain with the disagreement point as the vote of a voter chosen uniformly at random. This mechanism has a distortion of at most 1.66. We provide a lower bound of 1.38 for the distortion of this scheme. Further, we show that PB mechanisms that output a median of the votes of three voters chosen uniformly at random, have a distortion of at most 1.80.
Cite as
Mohak Goyal, Sukolsak Sakshuwong, Sahasrajit Sarmasarkar, and Ashish Goel. Low Sample Complexity Participatory Budgeting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 70:1-70:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{goyal_et_al:LIPIcs.ICALP.2023.70,
author = {Goyal, Mohak and Sakshuwong, Sukolsak and Sarmasarkar, Sahasrajit and Goel, Ashish},
title = {{Low Sample Complexity Participatory Budgeting}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {70:1--70:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.70},
URN = {urn:nbn:de:0030-drops-181223},
doi = {10.4230/LIPIcs.ICALP.2023.70},
annote = {Keywords: Social Choice, Participatory budgeting, Nash bargaining}
}
Document
Track A: Algorithms, Complexity and Games
The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly
Abstract
Algorithmic self-assembly occurs when components in a disorganized collection autonomously combine to form structures and, by their design and the dynamics of the system, are forced to intrinsically follow the execution of algorithms. Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-based self-assembly have blossomed into a mature theory with research strongly leveraging tools from computability theory, complexity theory, information theory, and graph theory to develop a wide range of models and to show that many are computationally universal, while also exposing a wide variety of powers and limitations of each. In addition to computational universality, the abstract Tile-Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this result fundamentally required non-deterministic tile attachments. This was later confirmed necessary when it was shown that the class of directed aTAM systems, those in which all possible sequences of tile attachments eventually result in the same terminal assembly, is not intrinsically universal (FOCS 2016). Furthermore, it was shown that the non-cooperative aTAM, where tiles only need to match on 1 side to bind rather than 2 or more, is not intrinsically universal (SODA 2014) nor computationally universal (STOC 2017). Building on these results to further investigate the impacts of other dynamics, Hader et al. examined several tile-assembly models which varied across (1) the numbers of dimensions used, (2) restrictions imposed on the diffusion of tiles through space, and (3) whether each system is directed, and determined which models exhibited intrinsic universality (SODA 2020). Such results have shed much light on the roles of various aspects of the dynamics of tile-assembly and their effects on the universality of each model. In this paper we extend that previous work to provide direct comparisons of the various models against each other by considering intrinsic simulations between models. Our results show that in some cases, one model is strictly more powerful than another, and in others, pairs of models have mutually exclusive capabilities. This direct comparison of models helps expose the impacts of these three important aspects of self-assembling systems, and further helps to define a hierarchy of tile-assembly models analogous to the hierarchies studied in traditional models of computation.
Cite as
Daniel Hader and Matthew J. Patitz. The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hader_et_al:LIPIcs.ICALP.2023.71,
author = {Hader, Daniel and Patitz, Matthew J.},
title = {{The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {71:1--71:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.71},
URN = {urn:nbn:de:0030-drops-181238},
doi = {10.4230/LIPIcs.ICALP.2023.71},
annote = {Keywords: Tile-Assembly, Tiles, aTAM, Intrinsic Simulation, Simulation}
}
Document
Track A: Algorithms, Complexity and Games
Parameter Estimation for Gibbs Distributions
Abstract
A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We will consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n].
The partition function is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log Z(β_max))/Z(β_min)
We develop a number of algorithms to estimate the counts c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²) samples for integer-valued distributions (ignoring some second-order terms and parameters), We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph.
Cite as
David G. Harris and Vladimir Kolmogorov. Parameter Estimation for Gibbs Distributions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 72:1-72:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{harris_et_al:LIPIcs.ICALP.2023.72,
author = {Harris, David G. and Kolmogorov, Vladimir},
title = {{Parameter Estimation for Gibbs Distributions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {72:1--72:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.72},
URN = {urn:nbn:de:0030-drops-181246},
doi = {10.4230/LIPIcs.ICALP.2023.72},
annote = {Keywords: Gibbs distribution, sampling}
}
Document
Track A: Algorithms, Complexity and Games
On Finding Constrained Independent Sets in Cycles
Abstract
A subset of [n] = {1,2,…,n} is called stable if it forms an independent set in the cycle on the vertex set [n]. In 1978, Schrijver proved via a topological argument that for all integers n and k with n ≥ 2k, the family of stable k-subsets of [n] cannot be covered by n-2k+1 intersecting families. We study two total search problems whose totality relies on this result.
In the first problem, denoted by Schrijver(n,k,m), we are given an access to a coloring of the stable k-subsets of [n] with m = m(n,k) colors, where m ≤ n-2k+1, and the goal is to find a pair of disjoint subsets that are assigned the same color. While for m = n-2k+1 the problem is known to be PPA-complete, we prove that for m < d ⋅ ⌊n/(2k+d-2)⌋, with d being any fixed constant, the problem admits an efficient algorithm. For m = ⌊n/2⌋-2k+1, we prove that the problem is efficiently reducible to the Kneser problem. Motivated by the relation between the problems, we investigate the family of unstable k-subsets of [n], which might be of independent interest.
In the second problem, called Unfair Independent Set in Cycle, we are given 𝓁 subsets V_1, …, V_𝓁 of [n], where 𝓁 ≤ n-2k+1 and |V_i| ≥ 2 for all i ∈ [𝓁], and the goal is to find a stable k-subset S of [n] satisfying the constraints |S ∩ V_i| ≤ |V_i|/2 for i ∈ [𝓁]. We prove that the problem is PPA-complete and that its restriction to instances with n = 3k is at least as hard as the Cycle plus Triangles problem, for which no efficient algorithm is known. On the contrary, we prove that there exists a constant c for which the restriction of the problem to instances with n ≥ c ⋅ k can be solved in polynomial time.
Cite as
Ishay Haviv. On Finding Constrained Independent Sets in Cycles. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 73:1-73:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{haviv:LIPIcs.ICALP.2023.73,
author = {Haviv, Ishay},
title = {{On Finding Constrained Independent Sets in Cycles}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {73:1--73:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.73},
URN = {urn:nbn:de:0030-drops-181254},
doi = {10.4230/LIPIcs.ICALP.2023.73},
annote = {Keywords: Schrijver graph, Kneser graph, Stable sets, PPA-completeness}
}
Document
Track A: Algorithms, Complexity and Games
Faster Submodular Maximization for Several Classes of Matroids
Abstract
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Though tight approximation algorithms for general matroid constraints exist in theory, the running times of such algorithms typically scale quadratically, and are not practical for truly large scale settings. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [Alina Ene and Huy L. Nguyen, 2019]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of 1-1/e-ε and both generalize and accelerate the results of Ene and Nguyen [Alina Ene and Huy L. Nguyen, 2019]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondrák [Ashwinkumar Badanidiyuru and Jan Vondrák, 2014].
To achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel Freeze operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [Stephen Alstrup et al., 2005] that maintains the maximum weight basis under insertions and deletions of elements in O(log n) time. This data structure needs to support certain subtree query and path update operations that are performed every insertion and deletion that are non-trivial to handle in conjunction. For the transversal matroid the Freeze operation corresponds to requiring the data structure to keep a certain set S of vertices matched, a property that we call S-stability. While there is a large body of work on dynamic matching algorithms, none are S-stable and maintain an approximate maximum weight matching under vertex updates. We give the first such algorithm for bipartite graphs with total running time linear (up to log factors) in the number of edges.
Cite as
Monika Henzinger, Paul Liu, Jan Vondrák, and Da Wei Zheng. Faster Submodular Maximization for Several Classes of Matroids. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 74:1-74:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{henzinger_et_al:LIPIcs.ICALP.2023.74,
author = {Henzinger, Monika and Liu, Paul and Vondr\'{a}k, Jan and Zheng, Da Wei},
title = {{Faster Submodular Maximization for Several Classes of Matroids}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {74:1--74:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.74},
URN = {urn:nbn:de:0030-drops-181267},
doi = {10.4230/LIPIcs.ICALP.2023.74},
annote = {Keywords: submodular optimization, dynamic data structures, matching algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Twin-Width of Planar Graphs Is at Most 8, and at Most 6 When Bipartite Planar
Abstract
Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. Having such a sequence at hand allows us to solve many otherwise hard problems efficiently. Graph classes of bounded twin-width, in which appropriate contraction sequences are efficiently constructible, are thus of interest in combinatorics and in computer science. However, we currently do not know in general how to obtain a witnessing contraction sequence of low width efficiently, and published upper bounds on the twin-width in non-trivial cases are often "astronomically large".
We focus on planar graphs, which are known to have bounded twin-width (already since the introduction of twin-width), but the first explicit "non-astronomical" upper bounds on the twin-width of planar graphs appeared just a year ago; namely the bound of at most 183 by Jacob and Pilipczuk [arXiv, January 2022], and 583 by Bonnet, Kwon and Wood [arXiv, February 2022]. Subsequent arXiv manuscripts in 2022 improved the bound down to 37 (Bekos et al.), 11 and 9 (both by Hliněný). We further elaborate on the approach used in the latter manuscripts, proving that the twin-width of every planar graph is at most 8, and construct a witnessing contraction sequence in linear time. Note that the currently best lower-bound planar example is of twin-width 7, by Král' and Lamaison [arXiv, September 2022]. We also prove that the twin-width of every bipartite planar graph is at most 6, and again construct a witnessing contraction sequence in linear time.
Cite as
Petr Hliněný and Jan Jedelský. Twin-Width of Planar Graphs Is at Most 8, and at Most 6 When Bipartite Planar. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 75:1-75:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hlineny_et_al:LIPIcs.ICALP.2023.75,
author = {Hlin\v{e}n\'{y}, Petr and Jedelsk\'{y}, Jan},
title = {{Twin-Width of Planar Graphs Is at Most 8, and at Most 6 When Bipartite Planar}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {75:1--75:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.75},
URN = {urn:nbn:de:0030-drops-181271},
doi = {10.4230/LIPIcs.ICALP.2023.75},
annote = {Keywords: twin-width, planar graph}
}
Document
Track A: Algorithms, Complexity and Games
A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing
Abstract
The Sparse Johnson-Lindenstrauss Transform of Kane and Nelson (SODA 2012) provides a linear dimensionality-reducing map A ∈ ℝ^{m × u} in 𝓁₂ that preserves distances up to distortion of 1 + ε with probability 1 - δ, where m = O(ε^{-2} log 1/δ) and each column of A has O(ε m) non-zero entries. The previous analyses of the Sparse Johnson-Lindenstrauss Transform all assumed access to a Ω(log 1/δ)-wise independent hash function. The main contribution of this paper is a more general analysis of the Sparse Johnson-Lindenstrauss Transform with less assumptions on the hash function. We also show that the Mixed Tabulation hash function of Dahlgaard, Knudsen, Rotenberg, and Thorup (FOCS 2015) satisfies the conditions of our analysis, thus giving us the first analysis of a Sparse Johnson-Lindenstrauss Transform that works with a practical hash function.
Cite as
Jakob Bæk Tejs Houen and Mikkel Thorup. A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 76:1-76:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{houen_et_al:LIPIcs.ICALP.2023.76,
author = {Houen, Jakob B{\ae}k Tejs and Thorup, Mikkel},
title = {{A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {76:1--76:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.76},
URN = {urn:nbn:de:0030-drops-181281},
doi = {10.4230/LIPIcs.ICALP.2023.76},
annote = {Keywords: dimensionality reduction, hashing, concentration bounds, moment bounds}
}
Document
Track A: Algorithms, Complexity and Games
Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm
Abstract
In this note, we describe a α_GW + Ω̃(1/d²)-factor approximation algorithm for Max-Cut on weighted graphs of degree ⩽ d. Here, α_GW ≈ 0.878 is the worst-case approximation ratio of the Goemans-Williamson rounding for Max-Cut. This improves on previous results for unweighted graphs by Feige, Karpinski, and Langberg [Feige et al., 2002] and Florén [Florén, 2016]. Our guarantee is obtained by a tighter analysis of the solution obtained by applying a natural local improvement procedure to the Goemans-Williamson rounding of the basic SDP strengthened with triangle inequalities.
Cite as
Jun-Ting Hsieh and Pravesh K. Kothari. Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 77:1-77:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hsieh_et_al:LIPIcs.ICALP.2023.77,
author = {Hsieh, Jun-Ting and Kothari, Pravesh K.},
title = {{Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {77:1--77:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.77},
URN = {urn:nbn:de:0030-drops-181291},
doi = {10.4230/LIPIcs.ICALP.2023.77},
annote = {Keywords: Max-Cut, approximation algorithm, semidefinite programming}
}
Document
Track A: Algorithms, Complexity and Games
Ellipsoid Fitting up to a Constant
Abstract
In [Saunderson, 2011; Saunderson et al., 2013], Saunderson, Parrilo, and Willsky asked the following elegant geometric question: what is the largest m = m(d) such that there is an ellipsoid in ℝ^d that passes through v_1, v_2, …, v_m with high probability when the v_is are chosen independently from the standard Gaussian distribution N(0,I_d)? The existence of such an ellipsoid is equivalent to the existence of a positive semidefinite matrix X such that v_i^⊤ X v_i = 1 for every 1 ⩽ i ⩽ m - a natural example of a random semidefinite program. SPW conjectured that m = (1-o(1)) d²/4 with high probability. Very recently, Potechin, Turner, Venkat and Wein [Potechin et al., 2022] and Kane and Diakonikolas [Kane and Diakonikolas, 2022] proved that m ≳ d²/log^O(1) d via a certain natural, explicit construction.
In this work, we give a substantially tighter analysis of their construction to prove that m ≳ d²/C for an absolute constant C > 0. This resolves one direction of the SPW conjecture up to a constant. Our analysis proceeds via the method of Graphical Matrix Decomposition that has recently been used to analyze correlated random matrices arising in various areas [Barak et al., 2019; Bafna et al., 2022]. Our key new technical tool is a refined method to prove singular value upper bounds on certain correlated random matrices that are tight up to absolute dimension-independent constants. In contrast, all previous methods that analyze such matrices lose logarithmic factors in the dimension.
Cite as
Jun-Ting Hsieh, Pravesh K. Kothari, Aaron Potechin, and Jeff Xu. Ellipsoid Fitting up to a Constant. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hsieh_et_al:LIPIcs.ICALP.2023.78,
author = {Hsieh, Jun-Ting and Kothari, Pravesh K. and Potechin, Aaron and Xu, Jeff},
title = {{Ellipsoid Fitting up to a Constant}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {78:1--78:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.78},
URN = {urn:nbn:de:0030-drops-181304},
doi = {10.4230/LIPIcs.ICALP.2023.78},
annote = {Keywords: Semidefinite programming, random matrices, average-case complexity}
}
Document
Track A: Algorithms, Complexity and Games
Finding Almost Tight Witness Trees
Abstract
This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.
Cite as
Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità. Finding Almost Tight Witness Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hyattdenesik_et_al:LIPIcs.ICALP.2023.79,
author = {Hyatt-Denesik, Dylan and Jabal Ameli, Afrouz and Sanit\`{a}, Laura},
title = {{Finding Almost Tight Witness Trees}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {79:1--79:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.79},
URN = {urn:nbn:de:0030-drops-181314},
doi = {10.4230/LIPIcs.ICALP.2023.79},
annote = {Keywords: Algorithms, Network Design, Approximation}
}
Document
Track A: Algorithms, Complexity and Games
Efficient Caching with Reserves via Marking
Abstract
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis - including potential functions and primal-dual techniques - give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [Ibrahimpur et al., 2022] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.
Cite as
Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Efficient Caching with Reserves via Marking. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 80:1-80:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ibrahimpur_et_al:LIPIcs.ICALP.2023.80,
author = {Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.},
title = {{Efficient Caching with Reserves via Marking}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {80:1--80:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.80},
URN = {urn:nbn:de:0030-drops-181328},
doi = {10.4230/LIPIcs.ICALP.2023.80},
annote = {Keywords: Approximation Algorithms, Online Algorithms, Caching}
}
Document
Track A: Algorithms, Complexity and Games
Rerouting Planar Curves and Disjoint Paths
Abstract
In this paper, we consider a transformation of k disjoint paths in a graph. For a graph and a pair of k disjoint paths 𝒫 and 𝒬 connecting the same set of terminal pairs, we aim to determine whether 𝒫 can be transformed to 𝒬 by repeatedly replacing one path with another path so that the intermediates are also k disjoint paths. The problem is called Disjoint Paths Reconfiguration. We first show that Disjoint Paths Reconfiguration is PSPACE-complete even when k = 2. On the other hand, we prove that, when the graph is embedded on a plane and all paths in 𝒫 and 𝒬 connect the boundaries of two faces, Disjoint Paths Reconfiguration can be solved in polynomial time. The algorithm is based on a topological characterization for rerouting curves on a plane using the algebraic intersection number. We also consider a transformation of disjoint s-t paths as a variant. We show that the disjoint s-t paths reconfiguration problem in planar graphs can be determined in polynomial time, while the problem is PSPACE-complete in general.
Cite as
Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, and Kenta Ozeki. Rerouting Planar Curves and Disjoint Paths. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ito_et_al:LIPIcs.ICALP.2023.81,
author = {Ito, Takehiro and Iwamasa, Yuni and Kakimura, Naonori and Kobayashi, Yusuke and Maezawa, Shun-ichi and Nozaki, Yuta and Okamoto, Yoshio and Ozeki, Kenta},
title = {{Rerouting Planar Curves and Disjoint Paths}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {81:1--81:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.81},
URN = {urn:nbn:de:0030-drops-181339},
doi = {10.4230/LIPIcs.ICALP.2023.81},
annote = {Keywords: Disjoint paths, combinatorial reconfiguration, planar graphs}
}
Document
Track A: Algorithms, Complexity and Games
Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra
Abstract
We prove that the computation of a combinatorial shortest path between two vertices of a graph associahedron, introduced by Carr and Devadoss, is NP-hard. This resolves an open problem raised by Cardinal. A graph associahedron is a generalization of the well-known associahedron. The associahedron is obtained as the graph associahedron of a path. It is a tantalizing and important open problem in theoretical computer science whether the computation of a combinatorial shortest path between two vertices of the associahedron can be done in polynomial time, which is identical to the computation of the flip distance between two triangulations of a convex polygon, and the rotation distance between two rooted binary trees. Our result shows that a certain generalized approach to tackling this open problem is not promising. As a corollary of our theorem, we prove that the computation of a combinatorial shortest path between two vertices of a polymatroid base polytope cannot be done in polynomial time unless P = NP. Since a combinatorial shortest path on the matroid base polytope can be computed in polynomial time, our result reveals an unexpected contrast between matroids and polymatroids.
Cite as
Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, and Yoshio Okamoto. Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 82:1-82:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ito_et_al:LIPIcs.ICALP.2023.82,
author = {Ito, Takehiro and Kakimura, Naonori and Kamiyama, Naoyuki and Kobayashi, Yusuke and Maezawa, Shun-ichi and Nozaki, Yuta and Okamoto, Yoshio},
title = {{Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {82:1--82:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.82},
URN = {urn:nbn:de:0030-drops-181344},
doi = {10.4230/LIPIcs.ICALP.2023.82},
annote = {Keywords: Graph associahedra, combinatorial shortest path, NP-hardness, polymatroids}
}
Document
Track A: Algorithms, Complexity and Games
Searching for Regularity in Bounded Functions
Abstract
Given a function f on F₂ⁿ, we study the following problem. What is the largest affine subspace 𝒰 such that when restricted to 𝒰, all the non-trivial Fourier coefficients of f are very small?
For the natural class of bounded Fourier degree d functions f: F₂ⁿ → [-1,1], we show that there exists an affine subspace of dimension at least Ω(n^{1/d!} k^{-2}), wherein all of f’s nontrivial Fourier coefficients become smaller than 2^{-k}. To complement this result, we show the existence of degree d functions with coefficients larger than 2^{-d log n} when restricted to any affine subspace of dimension larger than Ω(d n^{1/(d-1)}). In addition, we give explicit examples of functions with analogous but weaker properties.
Along the way, we provide multiple characterizations of the Fourier coefficients of functions restricted to subspaces of F₂ⁿ that may be useful in other contexts. Finally, we highlight applications and connections of our results to parity kill number and affine dispersers.
Cite as
Siddharth Iyer and Michael Whitmeyer. Searching for Regularity in Bounded Functions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 83:1-83:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{iyer_et_al:LIPIcs.ICALP.2023.83,
author = {Iyer, Siddharth and Whitmeyer, Michael},
title = {{Searching for Regularity in Bounded Functions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {83:1--83:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.83},
URN = {urn:nbn:de:0030-drops-181351},
doi = {10.4230/LIPIcs.ICALP.2023.83},
annote = {Keywords: regularity, bounded function, Boolean function, Fourier analysis}
}
Document
Track A: Algorithms, Complexity and Games
Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs
Abstract
We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with Õ(mn^{4/5}) worst-case update time processing arbitrary s,t-distance queries in Õ(n^{4/5}) time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.
Moreover, we give a Monte Carlo randomized fully dynamic reachability data structure processing single-edge updates in Õ(n√m) worst-case time and queries in O(√m) time. For sparse digraphs, such a tradeoff has only been previously described with amortized update time [Roditty and Zwick, SIAM J. Comp. 2008].
Cite as
Adam Karczmarz and Piotr Sankowski. Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 84:1-84:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{karczmarz_et_al:LIPIcs.ICALP.2023.84,
author = {Karczmarz, Adam and Sankowski, Piotr},
title = {{Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {84:1--84:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.84},
URN = {urn:nbn:de:0030-drops-181363},
doi = {10.4230/LIPIcs.ICALP.2023.84},
annote = {Keywords: dynamic shortest paths, dynamic reachability, dynamic transitive closure}
}
Document
Track A: Algorithms, Complexity and Games
New Additive Emulators
Abstract
For a given (possibly weighted) graph G = (V,E), an additive emulator H is a weighted graph in V × V that preserves the (all pairs) G-distances up to a small additive stretch. In their breakthrough result, [Abboud and Bodwin, STOC 2016] ruled out the possibility of obtaining o(n^{4/3})-size emulator with n^{o(1)} additive stretch. The focus of our paper is in the following question that has been explicitly stated in many of the prior work on this topic:
What is the minimal additive stretch attainable with linear size emulators?
The only known upper bound for this problem is given by an implicit construction of [Pettie, ICALP 2007] that provides a linear-size emulator with +Õ(n^{1/4}) stretch. No improvement on this problem has been shown since then.
In this work we improve upon the long standing additive stretch of Õ(n^{1/4}), by presenting constructions of linear-size emulators with Õ(n^{0.222}) additive stretch. Our constructions improve the state-of-the-art size vs. stretch tradeoff in the entire regime. For example, for every ε > 1/7, we provide +n^{f(ε)} emulators of size Õ(n^{1+ε}), for f(ε) = 1/5-3ε/5. This should be compared with the current bound of f(ε) = 1/4-3ε/4 by [Pettie, ICALP 2007].
The new emulators are based on an extended and optimized toolkit for computing weighted additive emulators with sublinear distance error. Our key construction provides a weighted modification of the well-known Thorup and Zwick emulators [SODA 2006]. We believe that this TZ variant might be of independent interest, especially for providing improved stretch for distant pairs.
Cite as
Shimon Kogan and Merav Parter. New Additive Emulators. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kogan_et_al:LIPIcs.ICALP.2023.85,
author = {Kogan, Shimon and Parter, Merav},
title = {{New Additive Emulators}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {85:1--85:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.85},
URN = {urn:nbn:de:0030-drops-181377},
doi = {10.4230/LIPIcs.ICALP.2023.85},
annote = {Keywords: Spanners, Emulators, Distance Preservers}
}
Document
Track A: Algorithms, Complexity and Games
Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems
Abstract
We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives such as makespan and weighted completion time. For many problems, we develop nearly-linear time approximation algorithms with approximation ratios matching the current best ones achieved in polynomial time.
Our main technique is linear programming relaxation. For the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. For the makespan objective, we develop a rounding algorithm with (2+ε)-approximation ratio. For the weighted completion time objective, we prove the LP is as strong as the rectangle LP used by Im and Li, leading to a nearly-linear time (1.45 + ε)-approximation for the problem.
For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the nearly-linear running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope.
Cite as
Shi Li. Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 86:1-86:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{li:LIPIcs.ICALP.2023.86,
author = {Li, Shi},
title = {{Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {86:1--86:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.86},
URN = {urn:nbn:de:0030-drops-181386},
doi = {10.4230/LIPIcs.ICALP.2023.86},
annote = {Keywords: Nearly-Linear Time, Sheduling, Approximation Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion
Abstract
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel’s principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series.
Cite as
Xiantao Li and Chunhao Wang. Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{li_et_al:LIPIcs.ICALP.2023.87,
author = {Li, Xiantao and Wang, Chunhao},
title = {{Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {87:1--87:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.87},
URN = {urn:nbn:de:0030-drops-181395},
doi = {10.4230/LIPIcs.ICALP.2023.87},
annote = {Keywords: Quantum algorithms, open quantum systems, Lindblad simulation}
}
Document
Track A: Algorithms, Complexity and Games
Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching
Abstract
We study the problem of solving linear program in the streaming model. Given a constraint matrix A ∈ ℝ^{m×n} and vectors b ∈ ℝ^m, c ∈ ℝ^n, we develop a space-efficient interior point method that optimizes solely on the dual program. To this end, we obtain efficient algorithms for various different problems:
- For general linear programs, we can solve them in Õ(√n log(1/ε)) passes and Õ(n²) space for an ε-approximate solution. To the best of our knowledge, this is the most efficient LP solver in streaming with no polynomial dependence on m for both space and passes.
- For bipartite graphs, we can solve the minimum vertex cover and maximum weight matching problem in Õ(√m) passes and Õ(n) space.
In addition to our space-efficient IPM, we also give algorithms for solving SDD systems and isolation lemma in Õ(n) spaces, which are the cornerstones for our graph results.
Cite as
S. Cliff Liu, Zhao Song, Hengjie Zhang, Lichen Zhang, and Tianyi Zhou. Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 88:1-88:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{liu_et_al:LIPIcs.ICALP.2023.88,
author = {Liu, S. Cliff and Song, Zhao and Zhang, Hengjie and Zhang, Lichen and Zhou, Tianyi},
title = {{Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {88:1--88:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.88},
URN = {urn:nbn:de:0030-drops-181408},
doi = {10.4230/LIPIcs.ICALP.2023.88},
annote = {Keywords: Convex optimization, interior point method, streaming algorithm}
}
Document
Track A: Algorithms, Complexity and Games
List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2
Abstract
Despite numerous results about the list decoding of Hamming-metric codes, development of list decoding on rank-metric codes is not as rapid as its counterpart. The bound of list decoding obeys the Gilbert-Varshamov bound in both the metrics. In the case of the Hamming-metric, the Gilbert-Varshamov bound is a trade-off among rate, decoding radius and alphabet size, while in the case of the rank-metric, the Gilbert-Varshamov bound is a trade-off among rate, decoding radius and column-to-row ratio (i.e., the ratio between the numbers of columns and rows). Hence, alphabet size and column-to-row ratio play a similar role for list decodability in each metric. In the case of the Hamming-metric, it is more challenging to list decode codes over smaller alphabets. In contrast, in the case of the rank-metric, it is more difficult to list decode codes with large column-to-row ratio. In particular, it is extremely difficult to list decode square matrix rank-metric codes (i.e., the column-to-row ratio is equal to 1).
The main purpose of this paper is to explicitly construct a class of rank-metric codes 𝒞 of rate R with the column-to-row ratio up to 2/3 and efficiently list decode these codes with decoding radius beyond the decoding radius (1-R)/2 (note that (1-R)/2 is at least half of relative minimum distance δ). In literature, the largest column-to-row ratio of rank-metric codes that can be efficiently list decoded beyond half of minimum distance is 1/2. Thus, it is greatly desired to efficiently design list decoding algorithms for rank-metric codes with the column-to-row ratio bigger than 1/2 or even close to 1. Our key idea is to compress an element of the field F_qⁿ into a smaller F_q-subspace via a linearized polynomial. Thus, the column-to-row ratio gets increased at the price of reducing the code rate. Our result shows that the compression technique is powerful and it has not been employed in the topic of list decoding of both the Hamming and rank metrics. Apart from the above algebraic technique, we follow some standard techniques to prune down the list. The algebraic idea enables us to pin down the message into a structured subspace of dimension linear in the number n of columns. This "periodic" structure allows us to pre-encode the message to prune down the list.
Cite as
Shu Liu, Chaoping Xing, and Chen Yuan. List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 89:1-89:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{liu_et_al:LIPIcs.ICALP.2023.89,
author = {Liu, Shu and Xing, Chaoping and Yuan, Chen},
title = {{List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {89:1--89:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.89},
URN = {urn:nbn:de:0030-drops-181416},
doi = {10.4230/LIPIcs.ICALP.2023.89},
annote = {Keywords: Coding theory, List-decoding, Rank-metric codes}
}
Document
Track A: Algorithms, Complexity and Games
Breaking the All Subsets Barrier for Min k-Cut
Abstract
In the Min k-Cut problem, the input is a graph G and an integer k. The task is to find a partition of the vertex set of G into k parts, while minimizing the number of edges that go between different parts of the partition. The problem is NP-complete, and admits a simple 3ⁿ⋅n^𝒪(1) time dynamic programming algorithm, which can be improved to a 2ⁿ⋅n^𝒪(1) time algorithm using the fast subset convolution framework by Björklund et al. [STOC'07]. In this paper we give an algorithm for Min k-Cut with running time 𝒪((2-ε)ⁿ), for ε > 10^{-50}. This is the first algorithm for Min k-Cut with running time 𝒪(cⁿ) for c < 2.
Cite as
Daniel Lokshtanov, Saket Saurabh, and Vaishali Surianarayanan. Breaking the All Subsets Barrier for Min k-Cut. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 90:1-90:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{lokshtanov_et_al:LIPIcs.ICALP.2023.90,
author = {Lokshtanov, Daniel and Saurabh, Saket and Surianarayanan, Vaishali},
title = {{Breaking the All Subsets Barrier for Min k-Cut}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {90:1--90:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.90},
URN = {urn:nbn:de:0030-drops-181422},
doi = {10.4230/LIPIcs.ICALP.2023.90},
annote = {Keywords: Exact algorithms, min k-cut, exponential algorithms, graph algorithms, k-way cut}
}
Document
Track A: Algorithms, Complexity and Games
A Tight (1.5+ε)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees
Abstract
In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the root of the tree such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1.
For the special case when all terminals have equal demands, a long line of research culminated in a quasi-polynomial time approximation scheme [Jayaprakash and Salavatipour, TALG 2023] and a polynomial time approximation scheme [Mathieu and Zhou, TALG 2023].
In this work, we study the general case when the terminals have arbitrary demands. Our main contribution is a polynomial time (1.5+ε)-approximation algorithm for the UCVRP on trees. This is the first improvement upon the 2-approximation algorithm more than 30 years ago. Our approximation ratio is essentially best possible, since it is NP-hard to approximate the UCVRP on trees to better than a 1.5 factor.
Cite as
Claire Mathieu and Hang Zhou. A Tight (1.5+ε)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 91:1-91:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{mathieu_et_al:LIPIcs.ICALP.2023.91,
author = {Mathieu, Claire and Zhou, Hang},
title = {{A Tight (1.5+\epsilon)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {91:1--91:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.91},
URN = {urn:nbn:de:0030-drops-181430},
doi = {10.4230/LIPIcs.ICALP.2023.91},
annote = {Keywords: approximation algorithms, capacitated vehicle routing, graph algorithms, combinatorial optimization}
}
Document
Track A: Algorithms, Complexity and Games
Online Demand Scheduling with Failovers
Abstract
Motivated by cloud computing applications, we study the problem of how to optimally deploy new hardware subject to both power and robustness constraints. To model the situation observed in large-scale data centers, we introduce the Online Demand Scheduling with Failover problem. There are m identical devices with capacity constraints. Demands come one-by-one and, to be robust against a device failure, need to be assigned to a pair of devices. When a device fails (in a failover scenario), each demand assigned to it is rerouted to its paired device (which may now run at increased capacity). The goal is to assign demands to the devices to maximize the total utilization subject to both the normal capacity constraints as well as these novel failover constraints. These latter constraints introduce new decision tradeoffs not present in classic assignment problems such as the Multiple Knapsack problem and AdWords.
In the worst-case model, we design a deterministic ≈ 1/2-competitive algorithm, and show this is essentially tight. To circumvent this constant-factor loss, which represents substantial capital losses for big cloud providers, we consider the stochastic arrival model, where all demands come i.i.d. from an unknown distribution. In this model we design an algorithm that achieves sub-linear additive regret (i.e. as OPT or m increases, the multiplicative competitive ratio goes to 1). This requires a combination of different techniques, including a configuration LP with a non-trivial post-processing step and an online monotone matching procedure introduced by Rhee and Talagrand.
Cite as
Konstantina Mellou, Marco Molinaro, and Rudy Zhou. Online Demand Scheduling with Failovers. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 92:1-92:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{mellou_et_al:LIPIcs.ICALP.2023.92,
author = {Mellou, Konstantina and Molinaro, Marco and Zhou, Rudy},
title = {{Online Demand Scheduling with Failovers}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {92:1--92:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.92},
URN = {urn:nbn:de:0030-drops-181443},
doi = {10.4230/LIPIcs.ICALP.2023.92},
annote = {Keywords: online algorithms, approximation algorithms, resource allocation}
}
Document
Track A: Algorithms, Complexity and Games
Faster Parameterized Algorithms for Modification Problems to Minor-Closed Classes
Abstract
Let G be a minor-closed graph class and let G be an n-vertex graph. We say that G is a k-apex of G if G contains a set S of at most k vertices such that G⧵S belongs to G. Our first result is an algorithm that decides whether G is a k-apex of G in time 2^poly(k)⋅n². This algorithm improves the previous one, given by Sau, Stamoulis, and Thilikos [ICALP 2020, TALG 2022], whose running time was 2^poly(k)⋅n³. The elimination distance of G to G, denoted by ed_G(G), is the minimum number of rounds required to reduce each connected component of G to a graph in G by removing one vertex from each connected component in each round. Bulian and Dawar [Algorithmica 2017] proved the existence of an FPT-algorithm, with parameter k, to decide whether ed_G(G) ≤ k. This algorithm is based on the computability of the minor-obstructions and its dependence on k is not explicit. We extend the techniques used in the first algorithm to decide whether ed_G(G) ≤ k in time 2^{2^{2^poly(k)}}⋅n². This is the first algorithm for this problem with an explicit parametric dependence in k. In the special case where G excludes some apex-graph as a minor, we give two alternative algorithms, one running in time 2^{2^O(k²log k)}⋅n² and one running in time 2^{poly(k)}⋅n³. As a stepping stone for these algorithms, we provide an algorithm that decides whether ed_G(G) ≤ k in time 2^O(tw⋅ k + tw log tw)⋅n, where tw is the treewidth of G. This algorithm combines the dynamic programming framework of Reidl, Rossmanith, Villaamil, and Sikdar [ICALP 2014] for the particular case where G contains only the empty graph (i.e., for treedepth) with the representative-based techniques introduced by Baste, Sau, and Thilikos [SODA 2020]. In all the algorithmic complexities above, poly is a polynomial function whose degree depends on G, while the hidden constants also depend on G. Finally, we provide explicit upper bounds on the size of the graphs in the minor-obstruction set of the class of graphs E_k(G) = {G ∣ ed_G(G) ≤ k}.
Cite as
Laure Morelle, Ignasi Sau, Giannos Stamoulis, and Dimitrios M. Thilikos. Faster Parameterized Algorithms for Modification Problems to Minor-Closed Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 93:1-93:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{morelle_et_al:LIPIcs.ICALP.2023.93,
author = {Morelle, Laure and Sau, Ignasi and Stamoulis, Giannos and Thilikos, Dimitrios M.},
title = {{Faster Parameterized Algorithms for Modification Problems to Minor-Closed Classes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {93:1--93:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.93},
URN = {urn:nbn:de:0030-drops-181458},
doi = {10.4230/LIPIcs.ICALP.2023.93},
annote = {Keywords: Graph minors, Parameterized algorithms, Graph modification problems, Vertex deletion, Elimination distance, Irrelevant vertex technique, Flat Wall Theorem, Obstructions}
}
Document
Track A: Algorithms, Complexity and Games
Nearly Tight Spectral Sparsification of Directed Hypergraphs
Abstract
Spectral hypergraph sparsification, an attempt to extend well-known spectral graph sparsification to hypergraphs, has been extensively studied over the past few years. For undirected hypergraphs, Kapralov, Krauthgamer, Tardos, and Yoshida (2022) have proved an ε-spectral sparsifier of the optimal O^*(n) size, where n is the number of vertices and O^* suppresses the ε^{-1} and log n factors. For directed hypergraphs, however, the optimal sparsifier size has not been known. Our main contribution is the first algorithm that constructs an O^*(n²)-size ε-spectral sparsifier for a weighted directed hypergraph. Our result is optimal up to the ε^{-1} and log n factors since there is a lower bound of Ω(n²) even for directed graphs. We also show the first non-trivial lower bound of Ω(n²/ε) for general directed hypergraphs. The basic idea of our algorithm is borrowed from the spanner-based sparsification for ordinary graphs by Koutis and Xu (2016). Their iterative sampling approach is indeed useful for designing sparsification algorithms in various circumstances. To demonstrate this, we also present a similar iterative sampling algorithm for undirected hypergraphs that attains one of the best size bounds, enjoys parallel implementation, and can be transformed to be fault-tolerant.
Cite as
Kazusato Oko, Shinsaku Sakaue, and Shin-ichi Tanigawa. Nearly Tight Spectral Sparsification of Directed Hypergraphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 94:1-94:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{oko_et_al:LIPIcs.ICALP.2023.94,
author = {Oko, Kazusato and Sakaue, Shinsaku and Tanigawa, Shin-ichi},
title = {{Nearly Tight Spectral Sparsification of Directed Hypergraphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {94:1--94:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.94},
URN = {urn:nbn:de:0030-drops-181469},
doi = {10.4230/LIPIcs.ICALP.2023.94},
annote = {Keywords: Spectral sparsification, (Directed) hypergraphs, Iterative sampling}
}
Document
Track A: Algorithms, Complexity and Games
The Communication Complexity of Set Intersection Under Product Distributions
Abstract
We consider a multiparty setting where k parties have private inputs X_1,…,X_k ⊆ [n] and wish to compute the intersection ⋂_{𝓁 =1}^k X_𝓁 of their sets, using as little communication as possible. This task generalizes the well-known problem of set disjointness, where the parties are required only to determine whether the intersection is empty or not. In the worst-case, it is known that the communication complexity of finding the intersection is the same as that of solving set disjointness, regardless of the size of the intersection: the cost of both problems is Ω(n log k + k) bits in the shared blackboard model, and Ω (nk) bits in the coordinator model.
In this work we consider a realistic setting where the parties' inputs are independent of one another, that is, the input is drawn from a product distribution. We show that this makes finding the intersection significantly easier than in the worst-case: only Θ̃((n^{1-1/k} (H(S) + 1)^{1/k}) + k) bits of communication are required, where {H}(S) is the Shannon entropy of the intersection S. We also show that the parties do not need to know the exact underlying input distribution; if we are given in advance O(n^{1/k}) samples from the underlying distribution μ, we can learn enough about μ to allow us to compute the intersection of an input drawn from μ using expected communication Θ̃((n^{1-1/k}𝔼[|S|]^{1/k}) + k), where |S| is the size of the intersection.
Cite as
Rotem Oshman and Tal Roth. The Communication Complexity of Set Intersection Under Product Distributions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{oshman_et_al:LIPIcs.ICALP.2023.95,
author = {Oshman, Rotem and Roth, Tal},
title = {{The Communication Complexity of Set Intersection Under Product Distributions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {95:1--95:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.95},
URN = {urn:nbn:de:0030-drops-181472},
doi = {10.4230/LIPIcs.ICALP.2023.95},
annote = {Keywords: Communication complexity, intersection, set disjointness}
}
Document
Track A: Algorithms, Complexity and Games
An Optimal Separation Between Two Property Testing Models for Bounded Degree Directed Graphs
Abstract
We revisit the relation between two fundamental property testing models for bounded-degree directed graphs: the bidirectional model in which the algorithms are allowed to query both the outgoing edges and incoming edges of a vertex, and the unidirectional model in which only queries to the outgoing edges are allowed. Czumaj, Peng and Sohler [STOC 2016] showed that for directed graphs with both maximum indegree and maximum outdegree upper bounded by d, any property that can be tested with query complexity O_{ε,d}(1) in the bidirectional model can be tested with n^{1-Ω_{ε,d}(1)} queries in the unidirectional model. In particular, {if the proximity parameter ε approaches 0, then the query complexity of the transformed tester in the unidirectional model approaches n}. It was left open if this transformation can be further improved or there exists any property that exhibits such an extreme separation.
We prove that testing subgraph-freeness in which the subgraph contains k source components, requires Ω(n^{1-1/k}) queries in the unidirectional model. This directly gives the first explicit properties that exhibit an O_{ε,d}(1) vs Ω(n^{1-f(ε,d)}) separation of the query complexities between the bidirectional model and unidirectional model, where f(ε,d) is a function that approaches 0 as ε approaches 0. Furthermore, our lower bound also resolves a conjecture by Hellweg and Sohler [ESA 2012] on the query complexity of testing k-star-freeness.
Cite as
Pan Peng and Yuyang Wang. An Optimal Separation Between Two Property Testing Models for Bounded Degree Directed Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 96:1-96:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{peng_et_al:LIPIcs.ICALP.2023.96,
author = {Peng, Pan and Wang, Yuyang},
title = {{An Optimal Separation Between Two Property Testing Models for Bounded Degree Directed Graphs}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {96:1--96:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.96},
URN = {urn:nbn:de:0030-drops-181480},
doi = {10.4230/LIPIcs.ICALP.2023.96},
annote = {Keywords: Graph property testing, Directed graphs, Lower bound, Subgraph-freeness}
}
Document
Track A: Algorithms, Complexity and Games
Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States
Abstract
This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee performs a binary POVM measurement to decide whether they win the game after receiving the quantum answers from the players. The quantum value of a fully quantum nonlocal game is the supremum of the probability that they win the game, where the supremum is taken over all the possible entangled states shared between the players and all the valid quantum operations performed by the players. The seminal work MIP^* = RE [Zhengfeng Ji et al., 2020; Zhengfeng Ji et al., 2020] implies that it is undecidable to approximate the quantum value of a fully nonlocal game. This still holds even if the players are only allowed to share (arbitrarily many copies of) maximally entangled states. This paper investigates the case that the shared maximally entangled states are noisy. We prove that there is a computable upper bound on the copies of noisy maximally entangled states for the players to win a fully quantum nonlocal game with a probability arbitrarily close to the quantum value. This implies that it is decidable to approximate the quantum values of these games. Hence, the hardness of approximating the quantum value of a fully quantum nonlocal game is not robust against the noise in the shared states.
This paper is built on the framework for the decidability of non-interactive simulations of joint distributions [Badih Ghazi et al., 2016; De et al., 2018; Ghazi et al., 2018] and generalizes the analogous result for nonlocal games in [Qin and Yao, 2021]. We extend the theory of Fourier analysis to the space of super-operators and prove several key results including an invariance principle and a dimension reduction for super-operators. These results are interesting in their own right and are believed to have further applications.
Cite as
Minglong Qin and Penghui Yao. Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 97:1-97:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{qin_et_al:LIPIcs.ICALP.2023.97,
author = {Qin, Minglong and Yao, Penghui},
title = {{Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {97:1--97:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.97},
URN = {urn:nbn:de:0030-drops-181499},
doi = {10.4230/LIPIcs.ICALP.2023.97},
annote = {Keywords: Fully quantum nonlocal games, Fourier analysis, Dimension reduction}
}
Document
Track A: Algorithms, Complexity and Games
Scheduling Under Non-Uniform Job and Machine Delays
Abstract
We study the problem of scheduling precedence-constrained jobs on heterogenous machines in the presence of non-uniform job and machine communication delays. We are given a set of n unit size precedence-ordered jobs, and a set of m related machines each with size m_i (machine i can execute at most m_i jobs at any time). Each machine i has an associated in-delay ρ^{in}_i and out-delay ρ^{out}_i. Each job v also has an associated in-delay ρ^{in}_v and out-delay ρ^{out}_v. In a schedule, job v may be executed on machine i at time t if each predecessor u of v is completed on i before time t or on any machine j before time t - (ρ^{in}_i + ρ^{out}_j + ρ^{out}_u + ρ^{in}_v). The objective is to construct a schedule that minimizes makespan, which is the maximum completion time over all jobs.
We consider schedules which allow duplication of jobs as well as schedules which do not. When duplication is allowed, we provide an asymptotic polylog(n)-approximation algorithm. This approximation is further improved in the setting with uniform machine speeds and sizes. Our best approximation for non-uniform delays is provided for the setting with uniform speeds, uniform sizes, and no job delays. For schedules with no duplication, we obtain an asymptotic polylog(n)-approximation for the above model, and a true polylog(n)-approximation for symmetric machine and job delays. These results represent the first polylogarithmic approximation algorithms for scheduling with non-uniform communication delays.
Finally, we consider a more general model, where the delay can be an arbitrary function of the job and the machine executing it: job v can be executed on machine i at time t if all of v’s predecessors are executed on i by time t-1 or on any machine by time t - ρ_{v,i}. We present an approximation-preserving reduction from the Unique Machines Precedence-constrained Scheduling (umps) problem, first defined in [Sami Davies et al., 2022], to this job-machine delay model. The reduction entails logarithmic hardness for this delay setting, as well as polynomial hardness if the conjectured hardness of umps holds.
This set of results is among the first steps toward cataloging the rich landscape of problems in non-uniform delay scheduling.
Cite as
Rajmohan Rajaraman, David Stalfa, and Sheng Yang. Scheduling Under Non-Uniform Job and Machine Delays. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 98:1-98:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{rajaraman_et_al:LIPIcs.ICALP.2023.98,
author = {Rajaraman, Rajmohan and Stalfa, David and Yang, Sheng},
title = {{Scheduling Under Non-Uniform Job and Machine Delays}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {98:1--98:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.98},
URN = {urn:nbn:de:0030-drops-181502},
doi = {10.4230/LIPIcs.ICALP.2023.98},
annote = {Keywords: Scheduling, Approximation Algorithms, Precedence Constraints, Communication Delay, Non-Uniform Delays}
}
Document
Track A: Algorithms, Complexity and Games
Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery
Abstract
In this work we consider the list-decodability and list-recoverability of arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable if every radius pn Hamming ball contains less than L codewords; (p,𝓁,L)_q-list-recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length 𝓁 and again stipulate that there be less than L codewords.
Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate (p,𝓁,L)_q-list-recoverable codes, the quantity we call the zero-rate threshold. Denoting this value by p_*, we in fact show that codes correcting a p_*+ε fraction of errors must have size O_ε(1), i.e., independent of n. Such a result is typically referred to as a "Plotkin bound." To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p_*-ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery.
Technically, proving the Plotkin bound boils down to demonstrating the Schur convexity of a certain function defined on the q-simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q-ary list-decoding; however, we point out that this earlier proof is flawed.
Cite as
Nicolas Resch, Chen Yuan, and Yihan Zhang. Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{resch_et_al:LIPIcs.ICALP.2023.99,
author = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan},
title = {{Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {99:1--99:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.99},
URN = {urn:nbn:de:0030-drops-181518},
doi = {10.4230/LIPIcs.ICALP.2023.99},
annote = {Keywords: Coding theory, List-decoding, List-recovery, Zero-rate thresholds}
}
Document
Track A: Algorithms, Complexity and Games
Convergence of the Number of Period Sets in Strings
Abstract
Consider words of length n. The set of all periods of a word of length n is a subset of {0,1,2,…,n-1}. However, any subset of {0,1,2,…,n-1} is not necessarily a valid set of periods. In a seminal paper in 1981, Guibas and Odlyzko proposed to encode the set of periods of a word into an n long binary string, called an autocorrelation, where a one at position i denotes the period i. They considered the question of recognizing a valid period set, and also studied the number of valid period sets for strings of length n, denoted κ_n. They conjectured that ln(κ_n) asymptotically converges to a constant times ln²(n). Although improved lower bounds for ln(κ_n)/ln²(n) were proposed in 2001, the question of a tight upper bound has remained open since Guibas and Odlyzko’s paper. Here, we exhibit an upper bound for this fraction, which implies its convergence and closes this longstanding conjecture. Moreover, we extend our result to find similar bounds for the number of correlations: a generalization of autocorrelations which encodes the overlaps between two strings.
Cite as
Eric Rivals, Michelle Sweering, and Pengfei Wang. Convergence of the Number of Period Sets in Strings. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 100:1-100:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{rivals_et_al:LIPIcs.ICALP.2023.100,
author = {Rivals, Eric and Sweering, Michelle and Wang, Pengfei},
title = {{Convergence of the Number of Period Sets in Strings}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {100:1--100:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.100},
URN = {urn:nbn:de:0030-drops-181527},
doi = {10.4230/LIPIcs.ICALP.2023.100},
annote = {Keywords: Autocorrelation, period, border, combinatorics, correlation, periodicity, upper bound, asymptotic convergence}
}
Document
Track A: Algorithms, Complexity and Games
Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability
Abstract
We show that feasibility of the t^th level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class ℒ_t of graphs such that graphs G and H are not distinguished by the t^th level of the Lasserre hierarchy if and only if they admit the same number of homomorphisms from any graph in ℒ_t. By analysing the treewidth of graphs in ℒ_t we prove that the 3t^th level of Sherali-Adams linear programming hierarchy is as strong as the t^th level of Lasserre. Moreover, we show that this is best possible in the sense that 3t cannot be lowered to 3t-1 for any t. The same result holds for the Lasserre hierarchy with non-negativity constraints, which we similarly characterise in terms of homomorphism indistinguishability over a family ℒ_t^+ of graphs. Additionally, we give characterisations of level-t Lasserre with non-negativity constraints in terms of logical equivalence and via a graph colouring algorithm akin to the Weisfeiler-Leman algorithm. This provides a polynomial time algorithm for determining if two given graphs are distinguished by the t^th level of the Lasserre hierarchy with non-negativity constraints.
Cite as
David E. Roberson and Tim Seppelt. Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 101:1-101:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{roberson_et_al:LIPIcs.ICALP.2023.101,
author = {Roberson, David E. and Seppelt, Tim},
title = {{Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {101:1--101:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.101},
URN = {urn:nbn:de:0030-drops-181531},
doi = {10.4230/LIPIcs.ICALP.2023.101},
annote = {Keywords: Lasserre hierarchy, homomorphism indistinguishability, Sherali-Adams hierarchy, treewidth, semidefinite programming, linear programming, graph isomorphism}
}
Document
Track A: Algorithms, Complexity and Games
Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem
Abstract
In the trace reconstruction problem, one is given many outputs (called traces) of a noise channel applied to the same input message x, and is asked to recover the input message. Common noise channels studied in the context of trace reconstruction include the deletion channel which deletes each bit w.p. δ, the insertion channel which inserts a G_j i.i.d. uniformly distributed bits before each bit of the input message (where G_j is i.i.d. geometrically distributed with parameter σ) and the symmetry channel which flips each bit of the input message i.i.d. w.p. γ.
De et al. and Nazarov and Peres [De et al., 2017; Nazarov and Peres, 2017] showed that any string x can be reconstructed from exp(O(n^{1/3})) traces. Holden et al. [Holden et al., 2018] adapted the techniques used to prove this upper bound, to construct an algorithm for average-case trace reconstruction from the insertion-deletion channel with a sample complexity of exp(O(log^{1/3} n)). However, it is not clear how to apply their techniques more generally and in particular for the recent worst-case upper bound of exp(Õ(n^{1/5})) shown by Chase [Chase, 2021] for the deletion channel.
We prove a general reduction from the average-case to smaller instances of a problem similar to worst-case and extend Chase’s upper-bound to this problem and to symmetry and insertion channels as well. Using this reduction and generalization of Chase’s bound, we introduce an algorithm for the average-case trace reconstruction from the symmetry-insertion-deletion channel with a sample complexity of exp(Õ(log^{1/5} n)).
Cite as
Ittai Rubinstein. Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{rubinstein:LIPIcs.ICALP.2023.102,
author = {Rubinstein, Ittai},
title = {{Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {102:1--102:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.102},
URN = {urn:nbn:de:0030-drops-181542},
doi = {10.4230/LIPIcs.ICALP.2023.102},
annote = {Keywords: Trace Reconstruction, Synchronization Channels, Computational Learning Theory, Computational Biology}
}
Document
Track A: Algorithms, Complexity and Games
The Support of Open Versus Closed Random Walks
Abstract
A closed random walk of length 𝓁 on an undirected and connected graph G = (V,E) is a random walk that returns to the start vertex at step 𝓁, and its properties have been recently related to problems in different mathematical fields, e.g., geometry and combinatorics (Jiang et al., Annals of Mathematics '21) and spectral graph theory (McKenzie et al., STOC '21). For instance, in the context of analyzing the eigenvalue multiplicity of graph matrices, McKenzie et al. show that, with high probability, the support of a closed random walk of length 𝓁 ⩾ 1 is Ω(𝓁^{1/5}) on any bounded-degree graph, and leaves as an open problem whether a stronger bound of Ω(𝓁^{1/2}) holds for any regular graph.
First, we show that the support of a closed random walk of length 𝓁 is at least Ω(𝓁^{1/2} / √{log n}) for any regular or bounded-degree graph on n vertices. Secondly, we prove for every 𝓁 ⩾ 1 the existence of a family of bounded-degree graphs, together with a start vertex such that the support is bounded by O(𝓁^{1/2}/√{log n}). Besides addressing the open problem of McKenzie et al., these two results also establish a subtle separation between closed random walks and open random walks, for which the support on any regular (or bounded-degree) graph is well-known to be Ω(𝓁^{1/2}) for all 𝓁 ⩾ 1. For irregular graphs, we prove that even if the start vertex is chosen uniformly, the support of a closed random walk may still be O(log 𝓁). This rules out a general polynomial lower bound in 𝓁 for all graphs. Finally, we apply our results on random walks to obtain new bounds on the multiplicity of the second largest eigenvalue of the adjacency matrices of graphs.
Cite as
Thomas Sauerwald, He Sun, and Danny Vagnozzi. The Support of Open Versus Closed Random Walks. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 103:1-103:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{sauerwald_et_al:LIPIcs.ICALP.2023.103,
author = {Sauerwald, Thomas and Sun, He and Vagnozzi, Danny},
title = {{The Support of Open Versus Closed Random Walks}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {103:1--103:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.103},
URN = {urn:nbn:de:0030-drops-181556},
doi = {10.4230/LIPIcs.ICALP.2023.103},
annote = {Keywords: support of random walks, eigenvalue multiplicity}
}
Document
Track A: Algorithms, Complexity and Games
Faster Matroid Partition Algorithms
Abstract
In the matroid partitioning problem, we are given k matroids ℳ₁ = (V, ℐ_1), … , ℳ_k = (V, ℐ_k) defined over a common ground set V of n elements, and we need to find a partitionable set S ⊆ V of largest possible cardinality, denoted by p. Here, a set S ⊆ V is called partitionable if there exists a partition (S_1, … , S_k) of S with S_i ∈ ℐ_i for i = 1, …, k. In 1986, Cunningham [Cunningham, 1986] presented a matroid partition algorithm that uses O(n p^{3/2} + k n) independence oracle queries, which was the previously known best algorithm. This query complexity is O(n^{5/2}) when k ≤ n.
Our main result is to present a matroid partition algorithm that uses Õ(k^{1/3} n p + k n) independence oracle queries, which is Õ(n^{7/3}) when k ≤ n. This improves upon previous Cunningham’s algorithm. To obtain this, we present a new approach edge recycling augmentation, which can be attained through new ideas: an efficient utilization of the binary search technique by Nguyễn [Nguyen, 2019] and Chakrabarty-Lee-Sidford-Singla-Wong [Chakrabarty et al., 2019] and a careful analysis of the number of independence oracle queries. Our analysis differs significantly from the one for matroid intersection algorithms, because of the parameter k. We also present a matroid partition algorithm that uses Õ((n + k) √p) rank oracle queries.
Cite as
Tatsuya Terao. Faster Matroid Partition Algorithms. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 104:1-104:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{terao:LIPIcs.ICALP.2023.104,
author = {Terao, Tatsuya},
title = {{Faster Matroid Partition Algorithms}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {104:1--104:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.104},
URN = {urn:nbn:de:0030-drops-181566},
doi = {10.4230/LIPIcs.ICALP.2023.104},
annote = {Keywords: Matroid Partition, Matroid Union, Combinatorial Optimization}
}
Document
Track A: Algorithms, Complexity and Games
Frameworks for Nonclairvoyant Network Design with Deadlines or Delay
Abstract
Clairvoyant network design with deadlines or delay has been studied extensively, culminating in an O(log n)-competitive general framework, where n is the number of possible request types (Azar and Touitou, FOCS 2020). In the nonclairvoyant setting, the problem becomes much harder, as Ω(√n) lower bounds are known for certain problems (Azar et al., STOC 2017). However, no frameworks are known for the nonclairvoyant setting, and previous work focuses only on specific problems, e.g., multilevel aggregation (Le et al., SODA 2023).
In this paper, we present the first nonclairvoyant frameworks for network design with deadlines or delay. These frameworks are nearly optimal: their competitive ratio is Õ(√n), which matches known lower bounds up to logarithmic factors.
Cite as
Noam Touitou. Frameworks for Nonclairvoyant Network Design with Deadlines or Delay. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 105:1-105:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{touitou:LIPIcs.ICALP.2023.105,
author = {Touitou, Noam},
title = {{Frameworks for Nonclairvoyant Network Design with Deadlines or Delay}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {105:1--105:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.105},
URN = {urn:nbn:de:0030-drops-181578},
doi = {10.4230/LIPIcs.ICALP.2023.105},
annote = {Keywords: Online, Deadlines, Delay, Network Design, Nonclairvoyant}
}
Document
Track A: Algorithms, Complexity and Games
Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth
Abstract
In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2^𝒪(tw)⋅|V(G)|, improving upon the running time 2^𝒪(tw²)⋅|V(G)|^𝒪(1) by Jansen, de Kroon, and Włodarczyk (STOC'21). When a tree decomposition of width tw is given, then the base of the exponent equals 2^{ω-1}⋅3 + 1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2^𝒪(tw log tw)⋅|V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.
Cite as
Michał Włodarczyk. Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 106:1-106:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{wlodarczyk:LIPIcs.ICALP.2023.106,
author = {W{\l}odarczyk, Micha{\l}},
title = {{Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {106:1--106:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.106},
URN = {urn:nbn:de:0030-drops-181585},
doi = {10.4230/LIPIcs.ICALP.2023.106},
annote = {Keywords: fixed-parameter tractability, treewidth, chordal graphs, interval graphs, matroids, representative families}
}
Document
Track A: Algorithms, Complexity and Games
The Wrong Direction of Jensen’s Inequality Is Algorithmically Right
Abstract
Let 𝒜 be an algorithm with expected running time e^X, conditioned on the value of some random variable X. We construct an algorithm A' with expected running time O (e^𝖤[X]), that fully executes 𝒜. In particular, an algorithm whose running time is a random variable T can be converted to one with expected running time O (e^𝖤[ln T]), which is never worse than O(𝖤[T]). No information about the distribution of X is required for the construction of 𝒜'.
Cite as
Or Zamir. The Wrong Direction of Jensen’s Inequality Is Algorithmically Right. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 107:1-107:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{zamir:LIPIcs.ICALP.2023.107,
author = {Zamir, Or},
title = {{The Wrong Direction of Jensen’s Inequality Is Algorithmically Right}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {107:1--107:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.107},
URN = {urn:nbn:de:0030-drops-181593},
doi = {10.4230/LIPIcs.ICALP.2023.107},
annote = {Keywords: algorithms, complexity, Jensen’s inequality}
}
Document
Track A: Algorithms, Complexity and Games
A Hyperbolic Extension of Kadison-Singer Type Results
Abstract
In 2013, Marcus, Spielman, and Srivastava resolved the famous Kadison-Singer conjecture. It states that for n independent random vectors v_1,⋯, v_n that have expected squared norm bounded by ε and are in the isotropic position in expectation, there is a positive probability that the determinant polynomial det(xI - ∑_{i=1}^n v_i v_i^⊤) has roots bounded by (1 + √ε)². An interpretation of the Kadison-Singer theorem is that we can always find a partition of the vectors v_1,⋯,v_n into two sets with a low discrepancy in terms of the spectral norm (in other words, rely on the determinant polynomial).
In this paper, we provide two results for a broader class of polynomials, the hyperbolic polynomials. Furthermore, our results are in two generalized settings:
- The first one shows that the Kadison-Singer result requires a weaker assumption that the vectors have a bounded sum of hyperbolic norms.
- The second one relaxes the Kadison-Singer result’s distribution assumption to the Strongly Rayleigh distribution. To the best of our knowledge, the previous results only support determinant polynomials [Anari and Oveis Gharan'14, Kyng, Luh and Song'20]. It is unclear whether they can be generalized to a broader class of polynomials. In addition, we also provide a sub-exponential time algorithm for constructing our results.
Cite as
Ruizhe Zhang and Xinzhi Zhang. A Hyperbolic Extension of Kadison-Singer Type Results. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 108:1-108:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{zhang_et_al:LIPIcs.ICALP.2023.108,
author = {Zhang, Ruizhe and Zhang, Xinzhi},
title = {{A Hyperbolic Extension of Kadison-Singer Type Results}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {108:1--108:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.108},
URN = {urn:nbn:de:0030-drops-181606},
doi = {10.4230/LIPIcs.ICALP.2023.108},
annote = {Keywords: Kadison-Singer conjecture, Hyperbolic polynomials, Strongly-Rayleigh distributions, Interlacing polynomials}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
On Semantically-Deterministic Automata
Abstract
Nondeterminism is a fundamental notion in Theoretical Computer Science. A nondeterministic automaton is semantically deterministic (SD) if different nondeterministic choices in the automaton lead to equivalent states. Semantic determinism is interesting as it is a natural relaxation of determinism, and as some applications of automata in formal methods require deterministic automata, yet in fact can use automata with some level of nondeterminism, tightly related to semantic determinism.
In the context of finite words, semantic determinism coincides with determinism, in the sense that every pruning of an SD automaton to a deterministic one results in an equivalent automaton. We study SD automata on infinite words, focusing on Büchi, co-Büchi, and weak automata. We show that there, while semantic determinism does not increase the expressive power, the combinatorial and computational properties of SD automata are very different from these of deterministic automata. In particular, SD Büchi and co-Büchi automata are exponentially more succinct than deterministic ones (in fact, also exponentially more succinct than history-deterministic automata), their complementation involves an exponential blow up, and decision procedures for them like universality and minimization are PSPACE-complete. For weak automata, we show that while an SD weak automaton need not be pruned to an equivalent deterministic one, it can be determinized to an equivalent deterministic weak automaton with the same state space, implying also efficient complementation and decision procedures for SD weak automata.
Cite as
Bader Abu Radi and Orna Kupferman. On Semantically-Deterministic Automata. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 109:1-109:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{aburadi_et_al:LIPIcs.ICALP.2023.109,
author = {Abu Radi, Bader and Kupferman, Orna},
title = {{On Semantically-Deterministic Automata}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {109:1--109:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.109},
URN = {urn:nbn:de:0030-drops-181610},
doi = {10.4230/LIPIcs.ICALP.2023.109},
annote = {Keywords: Automata on infinite words, Nondeterminism, Succinctness, Decision procedures}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Checking Refinement of Asynchronous Programs Against Context-Free Specifications
Abstract
In the language-theoretic approach to refinement verification, we check that the language of traces of an implementation all belong to the language of a specification. We consider the refinement verification problem for asynchronous programs against specifications given by a Dyck language. We show that this problem is EXPSPACE-complete - the same complexity as that of language emptiness and for refinement verification against a regular specification. Our algorithm uses several technical ingredients. First, we show that checking if the coverability language of a succinctly described vector addition system with states (VASS) is contained in a Dyck language is EXPSPACE-complete. Second, in the more technical part of the proof, we define an ordering on words and show a downward closure construction that allows replacing the (context-free) language of each task in an asynchronous program by a regular language. Unlike downward closure operations usually considered in infinite-state verification, our ordering is not a well-quasi-ordering, and we have to construct the regular language ab initio. Once the tasks can be replaced, we show a reduction to an appropriate VASS and use our first ingredient. In addition to the inherent theoretical interest, refinement verification with Dyck specifications captures common practical resource usage patterns based on reference counting, for which few algorithmic techniques were known.
Cite as
Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Checking Refinement of Asynchronous Programs Against Context-Free Specifications. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.110,
author = {Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg},
title = {{Checking Refinement of Asynchronous Programs Against Context-Free Specifications}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {110:1--110:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.110},
URN = {urn:nbn:de:0030-drops-181622},
doi = {10.4230/LIPIcs.ICALP.2023.110},
annote = {Keywords: Asynchronous programs, VASS, Dyck languages, Language inclusion, Refinement verification}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
On the Limits of Decision: the Adjacent Fragment of First-Order Logic
Abstract
We define the adjacent fragment AF of first-order logic, obtained by restricting the sequences of variables occurring as arguments in atomic formulas. The adjacent fragment generalizes (after a routine renaming) two-variable logic as well as the fluted fragment. We show that the adjacent fragment has the finite model property, and that its satisfiability problem is no harder than for the fluted fragment (and hence is Tower-complete). We further show that any relaxation of the adjacency condition on the allowed order of variables in argument sequences yields a logic whose satisfiability and finite satisfiability problems are undecidable. Finally, we study the effect of the adjacency requirement on the well-known guarded fragment (GF) of first-order logic. We show that the satisfiability problem for the guarded adjacent fragment (GA) remains 2ExpTime-hard, thus strengthening the known lower bound for GF.
Cite as
Bartosz Bednarczyk, Daumantas Kojelis, and Ian Pratt-Hartmann. On the Limits of Decision: the Adjacent Fragment of First-Order Logic. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 111:1-111:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bednarczyk_et_al:LIPIcs.ICALP.2023.111,
author = {Bednarczyk, Bartosz and Kojelis, Daumantas and Pratt-Hartmann, Ian},
title = {{On the Limits of Decision: the Adjacent Fragment of First-Order Logic}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {111:1--111:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.111},
URN = {urn:nbn:de:0030-drops-181632},
doi = {10.4230/LIPIcs.ICALP.2023.111},
annote = {Keywords: decidability, satisfiability, variable-ordered logics, complexity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Complexity of Presburger Arithmetic with Power or Powers
Abstract
We investigate expansions of Presburger arithmetic (Pa), i.e., the theory of the integers with addition and order, with additional structure related to exponentiation: either a function that takes a number to the power of 2, or a predicate 2^ℕ for the powers of 2. The latter theory, denoted Pa(2^ℕ(·)), was introduced by Büchi as a first attempt at characterizing the sets of tuples of numbers that can be expressed using finite automata; Büchi’s method does not give an elementary upper bound, and the complexity of this theory has been open. The former theory, denoted as Pa(λx.2^|x|), was shown decidable by Semenov; while the decision procedure for this theory differs radically from the automata-based method proposed by Büchi, Semenov’s method is also non-elementary. And in fact, the theory with the power function has a non-elementary lower bound. In this paper, we show that while Semenov’s and Büchi’s approaches yield non-elementary blow-ups for Pa(2^ℕ(·)), the theory is in fact decidable in triply exponential time, similarly to the best known quantifier-elimination algorithm for Pa. We also provide a NExpTime upper bound for the existential fragment of Pa(λx.2^|x|), a step towards a finer-grained analysis of its complexity. Both these results are established by analyzing a single parameterized satisfiability algorithm for Pa(λx.2^|x|), which can be specialized to either the setting of Pa(2^ℕ(·)) or the existential theory of Pa(λx.2^|x|). Besides the new upper bounds for the existential theory of Pa(λx.2^|x|) and Pa(2^ℕ(·)), we believe our algorithm provides new intuition for the decidability of these theories, and for the features that lead to non-elementary blow-ups.
Cite as
Michael Benedikt, Dmitry Chistikov, and Alessio Mansutti. The Complexity of Presburger Arithmetic with Power or Powers. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 112:1-112:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{benedikt_et_al:LIPIcs.ICALP.2023.112,
author = {Benedikt, Michael and Chistikov, Dmitry and Mansutti, Alessio},
title = {{The Complexity of Presburger Arithmetic with Power or Powers}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {112:1--112:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.112},
URN = {urn:nbn:de:0030-drops-181641},
doi = {10.4230/LIPIcs.ICALP.2023.112},
annote = {Keywords: arithmetic theories, exponentiation, decision procedures}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
A Dichotomy for Succinct Representations of Homomorphisms
Abstract
The task of computing homomorphisms between two finite relational structures A and B is a well-studied question with numerous applications. Since the set Hom(A, B) of all homomorphisms may be very large having a method of representing it in a succinct way, especially one which enables us to perform efficient enumeration and counting, could be extremely useful.
One simple yet powerful way of doing so is to decompose Hom(A, B) using union and Cartesian product. Such data structures, called d-representations, have been introduced by Olteanu and Závodný [Olteanu and Závodný, 2015] in the context of database theory. Their results also imply that if the treewidth of the left-hand side structure A is bounded, then a d-representation of polynomial size can be found in polynomial time. We show that for structures of bounded arity this is optimal: if the treewidth is unbounded then there are instances where the size of any d-representation is superpolynomial. Along the way we develop tools for proving lower bounds on the size of d-representations, in particular we define a notion of reduction suitable for this context and prove an almost tight lower bound on the size of d-representations of all k-cliques in a graph.
Cite as
Christoph Berkholz and Harry Vinall-Smeeth. A Dichotomy for Succinct Representations of Homomorphisms. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 113:1-113:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{berkholz_et_al:LIPIcs.ICALP.2023.113,
author = {Berkholz, Christoph and Vinall-Smeeth, Harry},
title = {{A Dichotomy for Succinct Representations of Homomorphisms}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {113:1--113:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.113},
URN = {urn:nbn:de:0030-drops-181653},
doi = {10.4230/LIPIcs.ICALP.2023.113},
annote = {Keywords: homomorphism problem, CSP, succinct representations, enumeration, lower bound, treewidth}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Nominal Topology for Data Languages
Abstract
We propose a novel topological perspective on data languages recognizable by orbit-finite nominal monoids. For this purpose, we introduce pro-orbit-finite nominal topological spaces. Assuming globally bounded support sizes, they coincide with nominal Stone spaces and are shown to be dually equivalent to a subcategory of nominal boolean algebras. Recognizable data languages are characterized as topologically clopen sets of pro-orbit-finite words. In addition, we explore the expressive power of pro-orbit-finite equations by establishing a nominal version of Reiterman’s pseudovariety theorem.
Cite as
Fabian Birkmann, Stefan Milius, and Henning Urbat. Nominal Topology for Data Languages. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 114:1-114:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{birkmann_et_al:LIPIcs.ICALP.2023.114,
author = {Birkmann, Fabian and Milius, Stefan and Urbat, Henning},
title = {{Nominal Topology for Data Languages}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {114:1--114:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.114},
URN = {urn:nbn:de:0030-drops-181662},
doi = {10.4230/LIPIcs.ICALP.2023.114},
annote = {Keywords: Nominal sets, Stone duality, Profinite space, Data languages}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Population Protocols with Unordered Data
Abstract
Population protocols form a well-established model of computation of passively mobile anonymous agents with constant-size memory. It is well known that population protocols compute Presburger-definable predicates, such as absolute majority and counting predicates. In this work, we initiate the study of population protocols operating over arbitrarily large data domains. More precisely, we introduce population protocols with unordered data as a formalism to reason about anonymous crowd computing over unordered sequences of data. We first show that it is possible to determine whether an unordered sequence from an infinite data domain has a datum with absolute majority. We then establish the expressive power of the "immediate observation" restriction of our model, namely where, in each interaction, an agent observes another agent who is unaware of the interaction.
Cite as
Michael Blondin and François Ladouceur. Population Protocols with Unordered Data. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{blondin_et_al:LIPIcs.ICALP.2023.115,
author = {Blondin, Michael and Ladouceur, Fran\c{c}ois},
title = {{Population Protocols with Unordered Data}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {115:1--115:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.115},
URN = {urn:nbn:de:0030-drops-181673},
doi = {10.4230/LIPIcs.ICALP.2023.115},
annote = {Keywords: Population protocols, unordered data, colored Petri nets}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Network Satisfaction Problems Solved by k-Consistency
Abstract
We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some k ∈ ℕ, is undecidable. For the important class of finite relation algebras A with a normal representation, however, the decidability of this problem remains open. We show that if A is symmetric and has a flexible atom, then the question whether NSP(A) can be solved by k-consistency, for some k ∈ ℕ, is decidable (even in polynomial time in the number of atoms of A). This result follows from a more general sufficient condition for the correctness of the k-consistency procedure for finite symmetric relation algebras. In our proof we make use of a result of Alexandr Kazda about finite binary conservative structures.
Cite as
Manuel Bodirsky and Simon Knäuer. Network Satisfaction Problems Solved by k-Consistency. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 116:1-116:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2023.116,
author = {Bodirsky, Manuel and Kn\"{a}uer, Simon},
title = {{Network Satisfaction Problems Solved by k-Consistency}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {116:1--116:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.116},
URN = {urn:nbn:de:0030-drops-181680},
doi = {10.4230/LIPIcs.ICALP.2023.116},
annote = {Keywords: Constraint Satisfaction, Computational Complexity, Relation Algebras, Network Satisfaction, Qualitative Reasoning, k-Consistency, Datalog}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Algebraic Recognition of Regular Functions
Abstract
We consider regular string-to-string functions, i.e. functions that are recognized by copyless streaming string transducers, or any of their equivalent models, such as deterministic two-way automata. We give yet another characterization, which is very succinct: finiteness-preserving functors from the category of semigroups to itself, together with a certain output function that is a natural transformation.
Cite as
Mikołaj Bojańczyk and Lê Thành Dũng (Tito) Nguyễn. Algebraic Recognition of Regular Functions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 117:1-117:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2023.117,
author = {Boja\'{n}czyk, Miko{\l}aj and Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito)},
title = {{Algebraic Recognition of Regular Functions}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {117:1--117:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.117},
URN = {urn:nbn:de:0030-drops-181697},
doi = {10.4230/LIPIcs.ICALP.2023.117},
annote = {Keywords: string transducers, semigroups, category theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
How to Play Optimally for Regular Objectives?
Abstract
This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where the goal of one of the two players is that eventually the sequence of colors along the play belongs to some regular language of finite words. We obtain different characterizations of the chromatic memory requirements for such objectives for both players, from which we derive complexity-theoretic statements: deciding whether there exist small memory structures sufficient to play optimally is NP-complete for both players. Some of our characterization results apply to a more general class of objectives: topologically closed and topologically open sets.
Cite as
Patricia Bouyer, Nathanaël Fijalkow, Mickael Randour, and Pierre Vandenhove. How to Play Optimally for Regular Objectives?. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 118:1-118:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bouyer_et_al:LIPIcs.ICALP.2023.118,
author = {Bouyer, Patricia and Fijalkow, Nathana\"{e}l and Randour, Mickael and Vandenhove, Pierre},
title = {{How to Play Optimally for Regular Objectives?}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {118:1--118:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.118},
URN = {urn:nbn:de:0030-drops-181700},
doi = {10.4230/LIPIcs.ICALP.2023.118},
annote = {Keywords: two-player games on graphs, strategy complexity, regular languages, finite-memory strategies, NP-completeness}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Monadic NIP in Monotone Classes of Relational Structures
Abstract
We prove that for any monotone class of finite relational structures, the first-order theory of the class is NIP in the sense of stability theory if, and only if, the collection of Gaifman graphs of structures in this class is nowhere dense. This generalises results previously known for graphs to relational structures and answers an open question posed by Adler and Adler (2014). The result is established by the application of Ramsey-theoretic techniques and shows that the property of being NIP is highly robust for monotone classes. We also show that the model-checking problem for first-order logic is intractable on any monotone class of structures that is not (monadically) NIP. This is a contribution towards the conjecture that the hereditary classes of structures admitting fixed-parameter tractable model-checking are precisely those that are monadically NIP.
Cite as
Samuel Braunfeld, Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos. Monadic NIP in Monotone Classes of Relational Structures. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 119:1-119:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{braunfeld_et_al:LIPIcs.ICALP.2023.119,
author = {Braunfeld, Samuel and Dawar, Anuj and Eleftheriadis, Ioannis and Papadopoulos, Aris},
title = {{Monadic NIP in Monotone Classes of Relational Structures}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {119:1--119:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.119},
URN = {urn:nbn:de:0030-drops-181712},
doi = {10.4230/LIPIcs.ICALP.2023.119},
annote = {Keywords: Model theory, finite model theory, structural graph theory, model-checking}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus
Abstract
We exhibit a strong connection between the matchgate formalism introduced by Valiant and the ZW-calculus of Coecke and Kissinger. This connection provides a natural compositional framework for matchgate theory as well as a direct combinatorial interpretation of the diagrams of ZW-calculus through the perfect matchings of their underlying graphs.
We identify a precise fragment of ZW-calculus, the planar W-calculus, that we prove to be complete and universal for matchgates, that are linear maps satisfying the matchgate identities. Computing scalars of the planar W-calculus corresponds to counting perfect matchings of planar graphs, and so can be carried in polynomial time using the FKT algorithm, making the planar W-calculus an efficiently simulable fragment of the ZW-calculus, in a similar way that the Clifford fragment is for ZX-calculus. This work opens new directions for the investigation of the combinatorial properties of ZW-calculus as well as the study of perfect matching counting through compositional diagrammatical technics.
Cite as
Titouan Carette, Etienne Moutot, Thomas Perez, and Renaud Vilmart. Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 120:1-120:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{carette_et_al:LIPIcs.ICALP.2023.120,
author = {Carette, Titouan and Moutot, Etienne and Perez, Thomas and Vilmart, Renaud},
title = {{Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {120:1--120:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.120},
URN = {urn:nbn:de:0030-drops-181726},
doi = {10.4230/LIPIcs.ICALP.2023.120},
annote = {Keywords: Perfect Matchings Counting, Quantum Computing, Matchgates, ZW-Calculus, String Diagrams, Completeness}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Deterministic Regular Functions of Infinite Words
Abstract
Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.
Cite as
Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic Regular Functions of Infinite Words. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 121:1-121:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{carton_et_al:LIPIcs.ICALP.2023.121,
author = {Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Winter, Sarah},
title = {{Deterministic Regular Functions of Infinite Words}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {121:1--121:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.121},
URN = {urn:nbn:de:0030-drops-181733},
doi = {10.4230/LIPIcs.ICALP.2023.121},
annote = {Keywords: infinite words, streaming string transducers, two-way transducers, monadic second-order logic, look-aheads, factorization forests}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Characterising Memory in Infinite Games
Abstract
This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (TheoretiCS 2023) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-ordered monotone universal graphs. We extend Ohlmann’s characterisation to encompass (finite or infinite) memory upper bounds.
We prove that objectives admitting optimal strategies with ε-memory less than m (a memory that cannot be updated when reading an ε-edge) are exactly those which admit well-founded monotone universal graphs whose antichains have size bounded by m. We also give a characterisation of chromatic memory by means of appropriate universal structures. Our results apply to finite as well as infinite memory bounds (for instance, to objectives with finite but unbounded memory, or with countable memory strategies).
We illustrate the applicability of our framework by carrying out a few case studies, we provide examples witnessing limitations of our approach, and we discuss general closure properties which follow from our results.
Cite as
Antonio Casares and Pierre Ohlmann. Characterising Memory in Infinite Games. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 122:1-122:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{casares_et_al:LIPIcs.ICALP.2023.122,
author = {Casares, Antonio and Ohlmann, Pierre},
title = {{Characterising Memory in Infinite Games}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {122:1--122:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.122},
URN = {urn:nbn:de:0030-drops-181740},
doi = {10.4230/LIPIcs.ICALP.2023.122},
annote = {Keywords: Infinite duration games, Memory, Universal graphs}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?
Abstract
Given a Boolean formula ϕ over n variables, the problem of model counting is to compute the number of solutions of ϕ. Model counting is a fundamental problem in computer science with wide-ranging applications in domains such as quantified information leakage, probabilistic reasoning, network reliability, neural network verification, and more. Owing to the #P-hardness of the problems, Stockmeyer initiated the study of the complexity of approximate counting. Stockmeyer showed that log n calls to an NP oracle are necessary and sufficient to achieve (ε,δ) guarantees. The hashing-based framework proposed by Stockmeyer has been very influential in designing practical counters over the past decade, wherein the SAT solver substitutes the NP oracle calls in practice. It is well known that an NP oracle does not fully capture the behavior of SAT solvers, as SAT solvers are also designed to provide satisfying assignments when a formula is satisfiable, without additional overhead. Accordingly, the notion of SAT oracle has been proposed to capture the behavior of SAT solver wherein given a Boolean formula, an SAT oracle returns a satisfying assignment if the formula is satisfiable or returns unsatisfiable otherwise. Since the practical state-of-the-art approximate counting techniques use SAT solvers, a natural question is whether an SAT oracle is more powerful than an NP oracle in the context of approximate model counting.
The primary contribution of this work is to study the relative power of the NP oracle and SAT oracle in the context of approximate model counting. The previous techniques proposed in the context of an NP oracle are weak to provide strong bounds in the context of SAT oracle since, in contrast to an NP oracle that provides only one bit of information, a SAT oracle can provide n bits of information. We therefore develop a new methodology to achieve the main result: a SAT oracle is no more powerful than an NP oracle in the context of approximate model counting.
Cite as
Diptarka Chakraborty, Sourav Chakraborty, Gunjan Kumar, and Kuldeep S. Meel. Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 123:1-123:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chakraborty_et_al:LIPIcs.ICALP.2023.123,
author = {Chakraborty, Diptarka and Chakraborty, Sourav and Kumar, Gunjan and Meel, Kuldeep S.},
title = {{Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {123:1--123:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.123},
URN = {urn:nbn:de:0030-drops-181750},
doi = {10.4230/LIPIcs.ICALP.2023.123},
annote = {Keywords: Model counting, Approximation, Satisfiability, NP oracle, SAT oracle}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Identity Problem in ℤ ≀ ℤ Is Decidable
Abstract
We consider semigroup algorithmic problems in the wreath product ℤ ≀ ℤ. Our paper focuses on two decision problems introduced by Choffrut and Karhumäki (2005): the Identity Problem (does a semigroup contain the neutral element?) and the Group Problem (is a semigroup a group?) for finitely generated sub-semigroups of ℤ ≀ ℤ. We show that both problems are decidable. Our result complements the undecidability of the Semigroup Membership Problem (does a semigroup contain a given element?) in ℤ ≀ ℤ shown by Lohrey, Steinberg and Zetzsche (ICALP 2013), and contributes an important step towards solving semigroup algorithmic problems in general metabelian groups.
Cite as
Ruiwen Dong. The Identity Problem in ℤ ≀ ℤ Is Decidable. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 124:1-124:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{dong:LIPIcs.ICALP.2023.124,
author = {Dong, Ruiwen},
title = {{The Identity Problem in \mathbb{Z} ≀ \mathbb{Z} Is Decidable}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {124:1--124:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.124},
URN = {urn:nbn:de:0030-drops-181768},
doi = {10.4230/LIPIcs.ICALP.2023.124},
annote = {Keywords: wreath product, algorithmic group theory, identity problem, polynomial semiring, positive coefficients}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes
Abstract
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they generalize notions such as nowhere denseness, bounded cliquewidth, and bounded twinwidth.
Our main result is the - to the best of our knowledge first - purely combinatorial characterization of monadically stable classes of graphs, in terms of a property dubbed flip-flatness. A class C of graphs is flip-flat if for every fixed radius r, every sufficiently large set of vertices of a graph G ∈ C contains a large subset of vertices with mutual distance larger than r, where the distance is measured in some graph G' that can be obtained from G by performing a bounded number of flips that swap edges and non-edges within a subset of vertices. Flip-flatness generalizes the notion of uniform quasi-wideness, which characterizes nowhere dense classes and had a key impact on the combinatorial and algorithmic treatment of nowhere dense classes. To obtain this result, we develop tools that also apply to the more general monadically NIP classes, based on the notion of indiscernible sequences from model theory. We show that in monadically stable and monadically NIP classes indiscernible sequences impose a strong combinatorial structure on their definable neighborhoods. All our proofs are constructive and yield efficient algorithms.
Cite as
Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk. Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 125:1-125:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{dreier_et_al:LIPIcs.ICALP.2023.125,
author = {Dreier, Jan and M\"{a}hlmann, Nikolas and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
title = {{Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {125:1--125:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.125},
URN = {urn:nbn:de:0030-drops-181779},
doi = {10.4230/LIPIcs.ICALP.2023.125},
annote = {Keywords: stability, NIP, combinatorial characterization, first-order model checking}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Black-Box Testing Liveness Properties of Partially Observable Stochastic Systems
Abstract
We study black-box testing for stochastic systems and arbitrary ω-regular specifications, explicitly including liveness properties. We are given a finite-state probabilistic system that we can only execute from the initial state. We have no information on the number of reachable states, or on the probabilities; further, we can only partially observe the states. The only action we can take is to restart the system. We design restart strategies guaranteeing that, if the specification is violated with non-zero probability, then w.p.1 the number of restarts is finite, and the infinite run executed after the last restart violates the specification. This improves on previous work that required full observability. We obtain asymptotically optimal upper bounds on the expected number of steps until the last restart. We conduct experiments on a number of benchmarks, and show that our strategies allow one to find violations in Markov chains much larger than the ones considered in previous work.
Cite as
Javier Esparza and Vincent P. Grande. Black-Box Testing Liveness Properties of Partially Observable Stochastic Systems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 126:1-126:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{esparza_et_al:LIPIcs.ICALP.2023.126,
author = {Esparza, Javier and Grande, Vincent P.},
title = {{Black-Box Testing Liveness Properties of Partially Observable Stochastic Systems}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {126:1--126:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.126},
URN = {urn:nbn:de:0030-drops-181785},
doi = {10.4230/LIPIcs.ICALP.2023.126},
annote = {Keywords: Partially observable Markov chains, \omega-regular properties, black-box testing}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Fine-Grained Complexity of Boolean Conjunctive Queries and Sum-Product Problems
Abstract
We study the fine-grained complexity of evaluating Boolean Conjunctive Queries and their generalization to sum-of-product problems over an arbitrary semiring. For these problems, we present a general semiring-oblivious reduction from the k-clique problem to any query structure (hypergraph). Our reduction uses the notion of embedding a graph to a hypergraph, first introduced by Marx [Dániel Marx, 2013]. As a consequence of our reduction, we can show tight conditional lower bounds for many classes of hypergraphs, including cycles, Loomis-Whitney joins, some bipartite graphs, and chordal graphs. These lower bounds have a dependence on what we call the clique embedding power of a hypergraph H, which we believe is a quantity of independent interest. We show that the clique embedding power is always less than the submodular width of the hypergraph, and present a decidable algorithm for computing it. We conclude with many open problems for future research.
Cite as
Austen Z. Fan, Paraschos Koutris, and Hangdong Zhao. The Fine-Grained Complexity of Boolean Conjunctive Queries and Sum-Product Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fan_et_al:LIPIcs.ICALP.2023.127,
author = {Fan, Austen Z. and Koutris, Paraschos and Zhao, Hangdong},
title = {{The Fine-Grained Complexity of Boolean Conjunctive Queries and Sum-Product Problems}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {127:1--127:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.127},
URN = {urn:nbn:de:0030-drops-181791},
doi = {10.4230/LIPIcs.ICALP.2023.127},
annote = {Keywords: Fine-grained complexity, conjunctive queries, semiring-oblivious reduction}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Flipper Games for Monadically Stable Graph Classes
Abstract
A class of graphs C is monadically stable if for every unary expansion Ĉ of C, one cannot encode - using first-order transductions - arbitrarily long linear orders in graphs from C. It is known that nowhere dense graph classes are monadically stable; these include classes of bounded maximum degree and classes that exclude a fixed topological minor. On the other hand, monadic stability is a property expressed in purely model-theoretic terms that is also suited for capturing structure in dense graphs.
In this work we provide a characterization of monadic stability in terms of the Flipper game: a game on a graph played by Flipper, who in each round can complement the edge relation between any pair of vertex subsets, and Localizer, who in each round is forced to restrict the game to a ball of bounded radius. This is an analog of the Splitter game, which characterizes nowhere dense classes of graphs (Grohe, Kreutzer, and Siebertz, J. ACM '17).
We give two different proofs of our main result. The first proof is based on tools borrowed from model theory, and it exposes an additional property of monadically stable graph classes that is close in spirit to definability of types. Also, as a byproduct, we show that monadic stability for graph classes coincides with monadic stability of existential formulas with two free variables, and we provide another combinatorial characterization of monadic stability via forbidden patterns. The second proof relies on the recently introduced notion of flip-flatness (Dreier, Mählmann, Siebertz, and Toruńczyk, arXiv 2206.13765) and provides an efficient algorithm to compute Flipper’s moves in a winning strategy.
Cite as
Jakub Gajarský, Nikolas Mählmann, Rose McCarty, Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, Sebastian Siebertz, Marek Sokołowski, and Szymon Toruńczyk. Flipper Games for Monadically Stable Graph Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 128:1-128:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2023.128,
author = {Gajarsk\'{y}, Jakub and M\"{a}hlmann, Nikolas and McCarty, Rose and Ohlmann, Pierre and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Siebertz, Sebastian and Soko{\l}owski, Marek and Toru\'{n}czyk, Szymon},
title = {{Flipper Games for Monadically Stable Graph Classes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {128:1--128:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.128},
URN = {urn:nbn:de:0030-drops-181804},
doi = {10.4230/LIPIcs.ICALP.2023.128},
annote = {Keywords: Stability theory, structural graph theory, games}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Regular Methods for Operator Precedence Languages
Abstract
The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time.
Cite as
Thomas A. Henzinger, Pavol Kebis, Nicolas Mazzocchi, and N. Ege Saraç. Regular Methods for Operator Precedence Languages. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 129:1-129:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{henzinger_et_al:LIPIcs.ICALP.2023.129,
author = {Henzinger, Thomas A. and Kebis, Pavol and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
title = {{Regular Methods for Operator Precedence Languages}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {129:1--129:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.129},
URN = {urn:nbn:de:0030-drops-181814},
doi = {10.4230/LIPIcs.ICALP.2023.129},
annote = {Keywords: operator precedence automata, syntactic congruence, antichain algorithm}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Positivity Problems for Reversible Linear Recurrence Sequences
Abstract
It is a longstanding open problem whether there is an algorithm to decide the Positivity Problem for linear recurrence sequences (LRS) over the integers, namely whether given such a sequence, all its terms are non-negative. Decidability is known for LRS of order 5 or less, i.e., for those sequences in which every new term depends linearly on the previous five (or fewer) terms. For simple LRS (i.e., those sequences whose characteristic polynomials have no repeated roots), decidability of Positivity is known up to order 9.
In this paper, we focus on the important subclass of reversible LRS, i.e., those integer LRS ⟨u_n⟩_{n=0}^∞ whose bi-infinite completion ⟨u_n⟩_{n=-∞}^∞ also takes exclusively integer values; a typical example is the classical Fibonacci (bi-)sequence ⟨ … , 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, … ⟩. Our main results are that Positivity is decidable for reversible LRS of order 11 or less, and for simple reversible LRS of order 17 or less.
Cite as
George Kenison, Joris Nieuwveld, Joël Ouaknine, and James Worrell. Positivity Problems for Reversible Linear Recurrence Sequences. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 130:1-130:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kenison_et_al:LIPIcs.ICALP.2023.130,
author = {Kenison, George and Nieuwveld, Joris and Ouaknine, Jo\"{e}l and Worrell, James},
title = {{Positivity Problems for Reversible Linear Recurrence Sequences}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {130:1--130:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.130},
URN = {urn:nbn:de:0030-drops-181821},
doi = {10.4230/LIPIcs.ICALP.2023.130},
annote = {Keywords: The Positivity Problem, Linear Recurrence Sequences, Verification}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality
Abstract
Seminal results establish that the coverability problem for Vector Addition Systems with States (VASS) is in EXPSPACE (Rackoff, '78) and is EXPSPACE-hard already under unary encodings (Lipton, '76). More precisely, Rosier and Yen later utilise Rackoff’s bounding technique to show that if coverability holds then there is a run of length at most n^{2^𝒪(d log d)}, where d is the dimension and n is the size of the given unary VASS. Earlier, Lipton showed that there exist instances of coverability in d-dimensional unary VASS that are only witnessed by runs of length at least n^{2^Ω(d)}. Our first result closes this gap. We improve the upper bound by removing the twice-exponentiated log(d) factor, thus matching Lipton’s lower bound. This closes the corresponding gap for the exact space required to decide coverability. This also yields a deterministic n^{2^𝒪(d)}-time algorithm for coverability. Our second result is a matching lower bound, that there does not exist a deterministic n^{2^o(d)}-time algorithm, conditioned upon the Exponential Time Hypothesis.
When analysing coverability, a standard proof technique is to consider VASS with bounded counters. Bounded VASS make for an interesting and popular model due to strong connections with timed automata. Withal, we study a natural setting where the counter bound is linear in the size of the VASS. Here the trivial exhaustive search algorithm runs in 𝒪(n^{d+1})-time. We give evidence to this being near-optimal. We prove that in dimension one this trivial algorithm is conditionally optimal, by showing that n^{2-o(1)}-time is required under the k-cycle hypothesis. In general fixed dimension d, we show that n^{d-2-o(1)}-time is required under the 3-uniform hyperclique hypothesis.
Cite as
Marvin Künnemann, Filip Mazowiecki, Lia Schütze, Henry Sinclair-Banks, and Karol Węgrzycki. Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 131:1-131:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kunnemann_et_al:LIPIcs.ICALP.2023.131,
author = {K\"{u}nnemann, Marvin and Mazowiecki, Filip and Sch\"{u}tze, Lia and Sinclair-Banks, Henry and W\k{e}grzycki, Karol},
title = {{Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {131:1--131:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.131},
URN = {urn:nbn:de:0030-drops-181834},
doi = {10.4230/LIPIcs.ICALP.2023.131},
annote = {Keywords: Vector Addition System, Coverability, Reachability, Fine-Grained Complexity, Exponential Time Hypothesis, k-Cycle Hypothesis, Hyperclique Hypothesis}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
First Order Logic on Pathwidth Revisited Again
Abstract
Courcelle’s celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height increases with each quantifier alternation in the formula. More devastatingly, this cannot be improved, under standard assumptions, even if we consider the much more restricted problem of deciding FO-expressible properties on trees.
In this paper we revisit this well-studied topic and identify a natural special case where the dependence of Courcelle’s theorem can, in fact, be improved. Specifically, we show that all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth). This is a rare example of treewidth and pathwidth having different complexity behaviors. Our result is also in sharp contrast with MSO logic on graphs of bounded pathwidth, where it is known that the dependence has to be non-elementary, under standard assumptions. Our work builds upon, and generalizes, a corresponding meta-theorem by Gajarský and Hliněný for the more restricted class of graphs of bounded tree-depth.
Cite as
Michael Lampis. First Order Logic on Pathwidth Revisited Again. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 132:1-132:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{lampis:LIPIcs.ICALP.2023.132,
author = {Lampis, Michael},
title = {{First Order Logic on Pathwidth Revisited Again}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {132:1--132:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.132},
URN = {urn:nbn:de:0030-drops-181848},
doi = {10.4230/LIPIcs.ICALP.2023.132},
annote = {Keywords: Algorithmic Meta-Theorems, FO logic, Pathwidth}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting
Abstract
At the core of the quest for a logic for Ptime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to tackle this problem is witnessed symmetric choice. It allows for choices from definable orbits certified by definable witnessing automorphisms.
We consider the extension of fixed-point logic with counting (IFPC) with witnessed symmetric choice (IFPC+WSC) and a further extension with an interpretation operator (IFPC+WSC+I). The latter operator evaluates a subformula in the structure defined by an interpretation. When similarly extending pure fixed-point logic (IFP), IFP+WSC+I simulates counting which IFP+WSC fails to do. For IFPC+WSC, it is unknown whether the interpretation operator increases expressiveness and thus allows studying the relation between WSC and interpretations beyond counting.
In this paper, we separate IFPC+WSC from IFPC+WSC+I by showing that IFPC+WSC is not closed under FO-interpretations. By the same argument, we answer an open question of Dawar and Richerby regarding non-witnessed symmetric choice in IFP. Additionally, we prove that nesting WSC-operators increases the expressiveness using the so-called CFI graphs. We show that if IFPC+WSC+I canonizes a particular class of base graphs, then it also canonizes the corresponding CFI graphs. This differs from various other logics, where CFI graphs provide difficult instances.
Cite as
Moritz Lichter. Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 133:1-133:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{lichter:LIPIcs.ICALP.2023.133,
author = {Lichter, Moritz},
title = {{Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {133:1--133:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.133},
URN = {urn:nbn:de:0030-drops-181858},
doi = {10.4230/LIPIcs.ICALP.2023.133},
annote = {Keywords: witnessed symmetric choice, interpretation, fixed-point logic, counting, CFI graphs, logic for PTime}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
On the Complexity of Diameter and Related Problems in Permutation Groups
Abstract
We prove that it is Π₂^𝖯-complete to verify whether the diameter of a given permutation group G = ⟨A⟩ is bounded by a unary encoded number k. This solves an open problem from a paper of Even and Goldreich, where the problem was shown to be NP-hard. Verifying whether the diameter is exactly k is complete for the class consisting of all intersections of a Π₂^𝖯-language and a Σ₂^𝖯-language. A similar result is shown for the length of a given permutation π, which is the minimal k such that π can be written as a product of at most k generators from A. Even and Goldreich proved that it is NP-complete to verify, whether the length of a given π is at most k (with k given in unary encoding). We show that it is DP-complete to verify whether the length is exactly k. Finally, we deduce from our result on the diameter that it is Π₂^𝖯-complete to check whether a given finite automaton with transitions labelled by permutations from S_n produces all permutations from S_n.
Cite as
Markus Lohrey and Andreas Rosowski. On the Complexity of Diameter and Related Problems in Permutation Groups. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 134:1-134:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{lohrey_et_al:LIPIcs.ICALP.2023.134,
author = {Lohrey, Markus and Rosowski, Andreas},
title = {{On the Complexity of Diameter and Related Problems in Permutation Groups}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {134:1--134:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.134},
URN = {urn:nbn:de:0030-drops-181864},
doi = {10.4230/LIPIcs.ICALP.2023.134},
annote = {Keywords: algorithms for finite groups, diameter of permutation groups, rational subsets in groups}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes
Abstract
We use model-theoretic tools originating from stability theory to derive a result we call the Finitary Substitute Lemma, which intuitively says the following. Suppose we work in a stable graph class 𝒞, and using a first-order formula φ with parameters we are able to define, in every graph G ∈ 𝒞, a relation R that satisfies some hereditary first-order assertion ψ. Then we are able to find a first-order formula φ' that has the same property, but additionally is finitary: there is finite bound k ∈ ℕ such that in every graph G ∈ 𝒞, different choices of parameters give only at most k different relations R that can be defined using φ'.
We use the Finitary Substitute Lemma to derive two corollaries about the existence of certain canonical decompositions in classes of well-structured graphs.
- We prove that in the Splitter game, which characterizes nowhere dense graph classes, and in the Flipper game, which characterizes monadically stable graph classes, there is a winning strategy for Splitter, respectively Flipper, that can be defined in first-order logic from the game history. Thus, the strategy is canonical.
- We show that for any fixed graph class 𝒞 of bounded shrubdepth, there is an 𝒪(n²)-time algorithm that given an n-vertex graph G ∈ 𝒞, computes in an isomorphism-invariant way a structure H of bounded treedepth in which G can be interpreted. A corollary of this result is an 𝒪(n²)-time isomorphism test and canonization algorithm for any fixed class of bounded shrubdepth.
Cite as
Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, and Szymon Toruńczyk. Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 135:1-135:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ohlmann_et_al:LIPIcs.ICALP.2023.135,
author = {Ohlmann, Pierre and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Toru\'{n}czyk, Szymon},
title = {{Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {135:1--135:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.135},
URN = {urn:nbn:de:0030-drops-181874},
doi = {10.4230/LIPIcs.ICALP.2023.135},
annote = {Keywords: Model Theory, Stability Theory, Shrubdepth, Nowhere Dense, Monadically Stable}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity
Abstract
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special class of probabilistic automata. We give a sound and complete Salomaa-style axiomatisation of bisimilarity of ProbGKAT expressions. Finally, we show that bisimilarity of ProbGKAT expressions can be decided in O(n³ log n) time via a generic partition refinement algorithm.
Cite as
Wojciech Różowski, Tobias Kappé, Dexter Kozen, Todd Schmid, and Alexandra Silva. Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 136:1-136:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{rozowski_et_al:LIPIcs.ICALP.2023.136,
author = {R\'{o}\.{z}owski, Wojciech and Kapp\'{e}, Tobias and Kozen, Dexter and Schmid, Todd and Silva, Alexandra},
title = {{Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {136:1--136:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.136},
URN = {urn:nbn:de:0030-drops-181880},
doi = {10.4230/LIPIcs.ICALP.2023.136},
annote = {Keywords: Kleene Algebra with Tests, program equivalence, completeness, coalgebra}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Action Codes
Abstract
We provide a new perspective on the problem how high-level state machine models with abstract actions can be related to low-level models in which these actions are refined by sequences of concrete actions. We describe the connection between high-level and low-level actions using action codes, a variation of the prefix codes known from coding theory. For each action code ℛ, we introduce a contraction operator α_ℛ that turns a low-level model ℳ into a high-level model, and a refinement operator ϱ_ℛ that transforms a high-level model 𝒩 into a low-level model. We establish a Galois connection ϱ_ℛ(𝒩) ⊑ ℳ ⇔ 𝒩 ⊑ α_ℛ(ℳ), where ⊑ is the well-known simulation preorder. For conformance, we typically want to obtain an overapproximation of model ℳ. To this end, we also introduce a concretization operator γ_ℛ, which behaves like the refinement operator but adds arbitrary behavior at intermediate points, giving us a second Galois connection α_ℛ(ℳ) ⊑ 𝒩 ⇔ ℳ ⊑ γ_ℛ(𝒩). Action codes may be used to construct adaptors that translate between concrete and abstract actions during learning and testing of Mealy machines. If Mealy machine ℳ models a black-box system then α_ℛ(ℳ) describes the behavior that can be observed by a learner/tester that interacts with this system via an adaptor derived from code ℛ. Whenever α_ℛ(ℳ) implements (or conforms to) 𝒩, we may conclude that ℳ implements (or conforms to) γ_ℛ (𝒩).
Almost all results, examples, and counter-examples are formalized in Coq.
Cite as
Frits Vaandrager and Thorsten Wißmann. Action Codes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 137:1-137:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{vaandrager_et_al:LIPIcs.ICALP.2023.137,
author = {Vaandrager, Frits and Wi{\ss}mann, Thorsten},
title = {{Action Codes}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {137:1--137:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.137},
URN = {urn:nbn:de:0030-drops-181895},
doi = {10.4230/LIPIcs.ICALP.2023.137},
annote = {Keywords: Automata, Models of Reactive Systems, LTS, Action Codes, Action Refinement, Action Contraction, Galois Connection, Model-Based Testing, Model Learning}
}