Dagstuhl Publishing
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RSS feed announcing the latest publications published by Schloss Dagstuhlen-en2010-06-082018-06-06http://www.dagstuhl.de/dagpub-rss.phpFront Matter, Table of Contents, Preface, Conference Organization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11358
Front Matter, Table of Contents, Preface, Conference OrganizationTue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11358Computing the Fourier Transformation over Temporal Data Streams (Invited Talk)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11359
In radio astronomy the sky is continuously scanned to collect frequency information about celestial objects. The inverse 2D Fourier transformation is used to generate images of the sky from the collected frequency information. We propose an algorithm that incrementally refines images by processing frequency information as it arrives in a temporal data stream. A direct implementation of the refinement with the discrete Fourier transformation requires O(N^2) complex multiplications to process an element of the stream. We propose a new algorithm that avoids recomputations and only requires O(N) complex multiplications.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11359From Unstructured Data to Narrative Abstractive Summaries (Invited Talk)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11360
To provide with easy and optimal access to digital information, narrative summaries must have a coherent and natural structure. Depending on how a summary is produced, a distinction can be made between extractive and abstractive summaries. Using an abstractive summarization approach, the relevant information (e.g., who? what?, when?, where?,...) could be fused together, leading to the generation of one or more new sentences. However, in order to do this it is necessary to obtain and process the temporal information in a text. A very effective way is the generation of timelines starting from multiple documents so that the generation of summaries is supported by the generated timeline, without losing the relevant temporal information of the texts. In this proposal, a enriched timeline is generated automatically, and the process of generating abstractive summaries is presented using this timeline as a basis [Barros et al., 2019]. Finally, potential applications of the automatic timeline generation would be presented, as for example its application to Fake News detection.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11360On the Computation of Nash Equilibria in Games on Graphs (Invited Talk)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11361
In this talk, I will show how one can characterize and compute Nash equilibria in multiplayer games played on graphs. I will present in particular a construction, called the suspect game construction, which allows to reduce the computation of Nash equilibria to the computation of winning strategies in a two-player zero-sum game.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11361A Modal Logic for Subject-Oriented Spatial Reasoning
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11362
We present a modal logic for representing and reasoning about space seen from the subject's perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11362Customizing BPMN Diagrams Using Timelines
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11363
BPMN (Business Process Model and Notation) is widely used standard modeling technique for representing Business Processes by using diagrams, but lacks in some aspects. Representing execution-dependent and time-dependent decisions in BPMN Diagrams may be a daunting challenge [Carlo Combi et al., 2017]. In many cases such constraints are omitted in order to preserve the simplicity and the readability of the process model. However, for purposes such as compliance checking, process mining, and verification, formalizing such constraints could be very useful. In this paper, we propose a novel approach for annotating BPMN Diagrams with Temporal Synchronization Rules borrowed from the timeline-based planning field. We discuss the expressivity of the proposed approach and show that it is able to capture a lot of complex temporally-related constraints without affecting the structure of BPMN diagrams. Finally, we provide a mapping from annotated BPMN diagrams to timeline-based planning problems that allows one to take advantage of the last twenty years of theoretical and practical developments in the field.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11363The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11364
We argue that European transport regulations can be formalized within the Sigma^1_1 fragment of monadic second order logic, and possibly weaker fragments including linear temporal logic. We consider several articles in the regulation to verify these claims.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11364Two-Dimensional Rule Language for Querying Sensor Log Data: A Framework and Use Cases
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11365
Motivated by two industrial use cases that involve detecting events of interest in (asynchronous) time series from sensors in manufacturing rigs and gas turbines, we design an expressive rule language DslD equipped with interval aggregate functions (such as weighted average over a time interval), Allen's interval relations and various metric constructs. We demonstrate how to model events in the uses cases in terms of DslD programs. We show that answering DslD queries in our use cases can be reduced to evaluating SQL queries. Our experiments with the use cases, carried out on the Apache Spark system, show that such SQL queries scale well on large real-world datasets.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11365Time-Aware Probabilistic Knowledge Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11366
The emergence of open information extraction as a tool for constructing and expanding knowledge graphs has aided the growth of temporal data, for instance, YAGO, NELL and Wikidata. While YAGO and Wikidata maintain the valid time of facts, NELL records the time point at which a fact is retrieved from some Web corpora. Collectively, these knowledge graphs (KG) store facts extracted from Wikipedia and other sources. Due to the imprecise nature of the extraction tools that are used to build and expand KG, such as NELL, the facts in the KG are weighted (a confidence value representing the correctness of a fact). Additionally, NELL can be considered as a transaction time KG because every fact is associated with extraction date. On the other hand, YAGO and Wikidata use the valid time model because they maintain facts together with their validity time (temporal scope). In this paper, we propose a bitemporal model (that combines transaction and valid time models) for maintaining and querying bitemporal probabilistic knowledge graphs. We study coalescing and scalability of marginal and MAP inference. Moreover, we show that complexity of reasoning tasks in atemporal probabilistic KG carry over to the bitemporal setting. Finally, we report our evaluation results of the proposed model.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11366Qualitative Reasoning and Data Mining
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11367
In this paper, we introduce a new data mining framework that is based on qualitative reasoning. We consider databases where the item domains are of different types, such as numerical values, time intervals and spatial regions. Then, for the considered tasks, we associate to each item a constraint network in a qualitative formalism representing the relations between all the pairs of objects of the database w.r.t. this item. In this context, the introduced data mining problems consist in discovering qualitative covariations between items. In a sense, our framework can be seen as a generalization of gradual itemset mining. In order to solve the introduced problem, we use a declarative approach based on the satisfiability problem in classical propositional logic (SAT). Indeed, we define SAT encodings where the models represent the desired patterns.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11367Recurrent Neural Networks Applied to GNSS Time Series for Denoising and Prediction
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11368
Global Navigation Satellite Systems (GNSS) are systems that continuously acquire data and provide position time series. Many monitoring applications are based on GNSS data and their efficiency depends on the capability in the time series analysis to characterize the signal content and/or to predict incoming coordinates. In this work we propose a suitable Network Architecture, based on Long Short Term Memory Recurrent Neural Networks, to solve two main tasks in GNSS time series analysis: denoising and prediction. We carry out an analysis on a synthetic time series, then we inspect two real different case studies and evaluate the results. We develop a non-deep network that removes almost the 50% of scattering from real GNSS time series and achieves a coordinate prediction with 1.1 millimeters of Mean Squared Error.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11368From Quantified CTL to QBF
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11369
QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several semantics exist for the quantifications: here, we work with the structure semantics, where the extra propositions label the Kripke structure (and not its execution tree), and the model-checking problem is known to be PSPACE-complete in this framework. We propose a model-checking algorithm for QCTL based on a reduction to QBF. We consider several reduction strategies, and we compare them with a prototype (based on the SMT-solver Z3) on several examples.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11369Towards Certified Model Checking for PLTL Using One-Pass Tableaux
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11370
The standard model checking setup analyses whether the given system specification satisfies a dedicated temporal property of the system, providing a positive answer here or a counter-example. At the same time, it is often useful to have an explicit proof that certifies the satisfiability. This is exactly what the certified model checking (CMC) has been introduced for. The paper argues that one-pass (context-based) tableau for PLTL can be efficiently used in the CMC setting, emphasising the following two advantages of this technique. First, the use of the context in which the eventualities occur, forces them to fulfil as soon as possible. Second, a dual to the tableau sequent calculus can be used to formalise the certificates. The combination of the one-pass tableau and the dual sequent calculus enables us to provide not only counter-examples for unsatisfied properties, but also proofs for satisfied properties that can be checked in a proof assistant. In addition, the construction of the tableau is enriched by an embedded solver, to which we dedicate those (propositional) computational tasks that are costly for the tableaux rules applied solely. The combination of the above techniques is particularly helpful to reason about large (system) specifications.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11370Minimisation of Models Satisfying CTL Formulas
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11371
We study the problem of minimisation of a given finite pointed Kripke model satisfying a given CTL formula, with the only objective to preserve the satisfaction of that formula in the resulting reduced model. We consider minimisations of the model with respect both to state-based redundancies and formula-based redundancies in that model. We develop a procedure computing all such minimisations, illustrate it with some examples, and provide some complexity analysis for it.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11371On the Utility of Neighbourhood Singleton-Style Consistencies for Qualitative Constraint-Based Spatial and Temporal Reasoning
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11372
A singleton-style consistency is a local consistency that verifies if each base relation (atom) of each constraint of a qualitative constraint network (QCN) can serve as a support with respect to the closure of that network under a (naturally) weaker local consistency. This local consistency is essential for tackling fundamental reasoning problems associated with QCNs, such as the satisfiability checking or the minimal labeling problem, but can suffer from redundant constraint checks, especially when those checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. In addition, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. We make an experimental evaluation with random and structured QCNs of Interval Algebra in the phase transition region to demonstrate the potential of our approach.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11372A Bounded Domain Property for an Expressive Fragment of First-Order Linear Temporal Logic
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11373
First-Order Linear Temporal Logic (FOLTL) is well-suited to specify infinite-state systems. However, FOLTL satisfiability is not even semi-decidable, thus preventing automated verification. To address this, a possible track is to constrain specifications to a decidable fragment of FOLTL, but known fragments are too restricted to be usable in practice. In this paper, we exhibit various fragments of increasing scope that provide a pertinent basis for abstract specification of infinite-state systems. We show that these fragments enjoy the Bounded Domain Property (any satisfiable FOLTL formula has a model with a finite, bounded FO domain), which provides a basis for complete, automated verification by reduction to LTL satisfiability. Finally, we present a simple case study illustrating the applicability and limitations of our results.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11373Hybrid SAT-Based Consistency Checking Algorithms for Simple Temporal Networks with Decisions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11374
A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN by adding decision time points to model temporal plans with decisions. A decision time point is a special kind of time point that once executed allows for deciding a truth value for an associated Boolean proposition. Furthermore, STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. Thus, an STND models a family of STNs each obtained as a projection of the initial STND onto a scenario. An STND is consistent if there exists a consistent scenario (i.e., a scenario such that the corresponding STN projection is consistent). Recently, a hybrid SAT-based consistency checking algorithm (HSCC) was proposed to check the consistency of an STND. Unfortunately, that approach lacks experimental evaluation and does not allow for the synthesis of all consistent scenarios. In this paper, we propose an incremental HSCC algorithm for STNDs that (i) is faster than the previous one and (ii) allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). Then, we carry out an experimental evaluation with KAPPA, a tool that we developed for STNDs. Finally, we prove that STNDs and disjunctive temporal networks (DTNs) are equivalent.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11374Synthesis of LTL Formulas from Natural Language Texts: State of the Art and Research Directions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11375
Linear temporal logic (LTL) is commonly used in model checking tasks; moreover, it is well-suited for the formalization of technical requirements. However, the correct specification and interpretation of temporal logic formulas require a strong mathematical background and can hardly be done by domain experts, who, instead, tend to rely on a natural language description of the intended system behaviour. In such situations, a system that is able to automatically translate English sentences into LTL formulas, and vice versa, would be of great help. While the task of rendering an LTL formula into a more readable English sentence may be carried out in a relatively easy way by properly parsing the formula, the converse is still an open problem, due to the inherent difficulty of interpreting free, natural language texts. Although several partial solutions have been proposed in the past, the literature still lacks a critical assessment of the work done. We address such a shortcoming, presenting the current state of the art for what concerns the English-to-LTL translation problem, and outlining some possible research directions.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11375Complexity Analysis of a Unifying Algorithm for Model Checking Interval Temporal Logic
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11376
The model-checking (MC) problem of Halpern and Shoham Interval Temporal Logic (HS) has been recently investigated in some papers and is known to be decidable. An intriguing open question concerns the exact complexity of the problem for full HS: it is at least EXPSPACE-hard, while the only known upper bound is non-elementary and is obtained by exploiting an abstract representation of Kripke structure paths called descriptors. In this paper we generalize the approach by providing a uniform framework for model-checking full HS and meaningful (almost maximal) fragments, where a specialized type of descriptor is defined for each fragment. We then devise a general MC alternating algorithm parameterized by the type of descriptor which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors (certificates). We analyze the time complexity of the algorithm and give, by non-trivial arguments, tight bounds on the length of certificates. For two types of descriptors, we obtain exponential upper and lower bounds which lead to an elementary MC algorithm for the related HS fragments. For the other types of descriptors, we provide non-elementary lower bounds. This last result addresses a question left open in some papers regarding the possibility of fixing an elementary upper bound on the size of the descriptors for full HS.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11376Simplifying Inductive Schemes in Temporal Logic
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11377
In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11377On Verifying Timed Hyperproperties
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11378
We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMTL, a timed extension of HyperLTL. Depending on whether interleaving of events in different traces is allowed, two possible semantics can be defined for timed hyperproperties: synchronous and asynchronous. While the satisfiability problem can be decided similarly as for HyperLTL regardless of the choice of semantics, we show that the model-checking problem for HyperMTL, unless the specification is alternation-free, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMTL with quantifier alternations is possible under certain conditions in the synchronous semantics, or when there is a fixed bound on the length of the time domain.Tue, 15 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11378Front Matter, Table of Contents, Preface, Conference Organization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11307
Front Matter, Table of Contents, Preface, Conference OrganizationFri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11307Consensus with Max Registers
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11308
We consider the problem of implementing randomized wait-free consensus from max registers under the assumption of an oblivious adversary. We show that max registers solve m-valued consensus for arbitrary m in expected O(log^* n) steps per process, beating the Omega(log m/log log m) lower bound for ordinary registers when m is large and the best previously known O(log log n) upper bound when m is small. A simple max-register implementation based on double-collect snapshots translates this result into an O(n log n) expected step implementation of m-valued consensus from n single-writer registers, improving on the best previously-known bound of O(n log^2 n) for single-writer registers.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11308Long-Lived Counters with Polylogarithmic Amortized Step Complexity
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11310
A shared-memory counter is a well-studied and widely-used concurrent object. It supports two operations: An Inc operation that increases its value by 1 and a Read operation that returns its current value. Jayanti, Tan and Toueg [Jayanti et al., 2000] proved a linear lower bound on the worst-case step complexity of obstruction-free implementations, from read and write operations, of a large class of shared objects that includes counters. The lower bound leaves open the question of finding counter implementations with sub-linear amortized step complexity.In this paper, we address this gap. We present the first wait-free n-process counter, implemented using only read and write operations, whose amortized operation step complexity is O(log^2 n) in all executions. This is the first non-blocking read/write counter algorithm that provides sub-linear amortized step complexity in executions of arbitrary length. Since a logarithmic lower bound on the amortized step complexity of obstruction-free counter implementations exists, our upper bound is optimal up to a logarithmic factor.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11310Distributed Algorithms for Low Stretch Spanning Trees
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11311
Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch. Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log^{3} n), where n is the number of nodes in the graph. If the graph is unweighted, then this algorithm can be implemented to run in O(D) rounds, where D is the hop-diameter of the graph, thus being asymptotically optimal. In the weighted case, the run-time of our algorithm matches the currently best known bound for exact distance computations, i.e., O~ (min{sqrt{n D}, sqrt{n} D^{1 / 4} + n^{3 / 5} + D}). We stress that this is the first distributed construction of spanning trees leading to poly-logarithmic expected stretch with non-trivial running time.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11311Optimal Distributed Covering Algorithms
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11312
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+epsilon). Let Delta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log{Delta} / log log Delta) rounds, for constants epsilon in (0,1] and f in N^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms.For constant values of f and epsilon, our algorithm improves over the (f+epsilon)-approximation algorithm of [Fabian Kuhn et al., 2006] whose running time is O(log Delta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(f log n) rounds, improving over the classical result of [Samir Khuller et al., 1994] that achieves a running time of O(f log^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of [Koufogiannakis and Young, 2011].We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f+epsilon)-approximate integral solution in O((1+f/log n)* ((log Delta)/(log log Delta) + (f * log M)^{1.01}* log epsilon^{-1}* (log Delta)^{0.01})) rounds, where f bounds the number of variables in a constraint, Delta bounds the number of constraints a variable appears in, and M=max {1, ceil[1/a_{min}]}, where a_{min} is the smallest normalized constraint coefficient. This improves over the results of [Fabian Kuhn et al., 2006] for the integral case, which combined with rounding achieves the same guarantees in O(epsilon^{-4}* f^4 * log f * log(M * Delta)) rounds.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11312Parameterized Distributed Algorithms
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11313
In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds.Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11313Message Reduction in the LOCAL Model Is a Free Lunch
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11314
A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11314On the Computational Power of Radio Channels
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11315
Radio networks can be a challenging platform for which to develop distributed algorithms, because the network nodes must contend for a shared channel. In some cases, though, the shared medium is an advantage rather than a disadvantage: for example, many radio network algorithms cleverly use the shared channel to approximate the degree of a node, or estimate the contention. In this paper we ask how far the inherent power of a shared radio channel goes, and whether it can efficiently compute "classicaly hard" functions such as Majority, Approximate Sum, and Parity.Using techniques from circuit complexity, we show that in many cases, the answer is "no". We show that simple radio channels, such as the beeping model or the channel with collision-detection, can be approximated by a low-degree polynomial, which makes them subject to known lower bounds on functions such as Parity and Majority; we obtain round lower bounds of the form Omega(n^{delta}) on these functions, for delta in (0,1). Next, we use the technique of random restrictions, used to prove AC^0 lower bounds, to prove a tight lower bound of Omega(1/epsilon^2) on computing a (1 +/- epsilon)-approximation to the sum of the nodes' inputs. Our techniques are general, and apply to many types of radio channels studied in the literature.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11315Space-Optimal Naming in Population Protocols
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11316
The distributed naming problem, assigning unique names to the nodes in a distributed system, is a fundamental task. This problem is nontrivial, especially when the amount of memory available for the task is low, and when requirements for fault-tolerance are added.The considered distributed communication model is population protocols. In this model, a priori anonymous and indistinguishable mobile nodes (called agents), communicate in pairs and in an asynchronous manner (according to a fairness condition). Fault-tolerance is addressed through self-stabilization, in terms of arbitrary initialization of agents.This work comprises a comprehensive study of the necessary and sufficient state space conditions for naming. The problem is studied under various combinations of model assumptions: weak or global fairness, arbitrary or uniform initialization of agents, existence or absence of a distinguishable agent (arbitrarily initialized or not), possibility of breaking symmetry in pair-wise interactions (symmetric or asymmetric transitions). For each possible combination of these assumptions, either an impossibility is proven or the necessary exact number of states (per mobile agent) is determined and an appropriate space-optimal naming protocol is presented.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11316Erasure Correction for Noisy Radio Networks
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11317
The radio network model is a well-studied model of wireless, multi-hop networks. However, radio networks make the strong assumption that messages are delivered deterministically. The recently introduced noisy radio network model relaxes this assumption by dropping messages independently at random.In this work we quantify the relative computational power of noisy radio networks and classic radio networks. In particular, given a non-adaptive protocol for a fixed radio network we show how to reliably simulate this protocol if noise is introduced with a multiplicative cost of poly(log Delta, log log n) rounds where n is the number nodes in the network and Delta is the max degree. Moreover, we demonstrate that, even if the simulated protocol is not non-adaptive, it can be simulated with a multiplicative O(Delta log ^2 Delta) cost in the number of rounds. Lastly, we argue that simulations with a multiplicative overhead of o(log Delta) are unlikely to exist by proving that an Omega(log Delta) multiplicative round overhead is necessary under certain natural assumptions.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11317Reachability and Shortest Paths in the Broadcast CONGEST Model
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11318
In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter D of the underlying network is constant.We show that for the case where D = 1 there is, quite surprisingly, a very simple algorithm that solves the reachability problem in 1(!) round. In contrast, for networks with D = 2, we show that any distributed algorithm (possibly randomized) for this problem requires Omega(sqrt{n/ log{n}}) rounds. Our results therefore completely resolve (up to a small polylog factor) the complexity of the single-source reachability problem for a wide range of diameters.Furthermore, we show that when D = 1, it is even possible to get an almost 3 - approximation for the all-pairs shortest path problem (for directed unweighted graphs) in just 2 rounds. We also prove a stronger lower bound of Omega(sqrt{n}) for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is 2. As far as we know this is the first lower bound that achieves Omega(sqrt{n}) for this problem.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11318On the Round Complexity of Randomized Byzantine Agreement
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11319
We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)]. 2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1). 3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI).The third bound essentially matches the recent protocol of Micali (ITCS'17) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11319Trade-Offs in Distributed Interactive Proofs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11320
The study of interactive proofs in the context of distributed network computing is a novel topic, recently introduced by Kol, Oshman, and Saxena [PODC 2018]. In the spirit of sequential interactive proofs theory, we study the power of distributed interactive proofs. This is achieved via a series of results establishing trade-offs between various parameters impacting the power of interactive proofs, including the number of interactions, the certificate size, the communication complexity, and the form of randomness used. Our results also connect distributed interactive proofs with the established field of distributed verification. In general, our results contribute to providing structure to the landscape of distributed interactive proofs.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11320The Capacity of Smartphone Peer-To-Peer Networks
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11321
We study three capacity problems in the mobile telephone model, a network abstraction that models the peer-to-peer communication capabilities implemented in most commodity smartphone operating systems. The capacity of a network expresses how much sustained throughput can be maintained for a set of communication demands, and is therefore a fundamental bound on the usefulness of a network. Because of this importance, wireless network capacity has been active area of research for the last two decades. The three capacity problems that we study differ in the structure of the communication demands. The first problem is pairwise capacity, where the demands are (source, destination) pairs. Pairwise capacity is one of the most classical definitions, as it was analyzed in the seminal paper of Gupta and Kumar on wireless network capacity. The second problem we study is broadcast capacity, in which a single source must deliver packets to all other nodes in the network. Finally, we turn our attention to all-to-all capacity, in which all nodes must deliver packets to all other nodes. In all three of these problems we characterize the optimal achievable throughput for any given network, and design algorithms which asymptotically match this performance. We also study these problems in networks generated randomly by a process introduced by Gupta and Kumar, and fully characterize their achievable throughput. Interestingly, the techniques that we develop for all-to-all capacity also allow us to design a one-shot gossip algorithm that runs within a polylogarithmic factor of optimal in every graph. This largely resolves an open question from previous work on the one-shot gossip problem in this model.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11321Sublinear-Time Distributed Algorithms for Detecting Small Cliques and Even Cycles
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11322
In this paper we give sublinear-time distributed algorithms in the CONGEST model for subgraph detection for two classes of graphs: cliques and even-length cycles. We show for the first time that all copies of 4-cliques and 5-cliques in the network graph can be listed in sublinear time, O(n^{5/6+o(1)}) rounds and O(n^{21/22+o(1)}) rounds, respectively. Prior to our work, it was not known whether it was possible to even check if the network contains a 4-clique or a 5-clique in sublinear time.For even-length cycles, C_{2k}, we give an improved sublinear-time algorithm, which exploits a new connection to extremal combinatorics. For example, for 6-cycles we improve the running time from O~(n^{5/6}) to O~(n^{3/4}) rounds. We also show two obstacles on proving lower bounds for C_{2k}-freeness: First, we use the new connection to extremal combinatorics to show that the current lower bound of Omega~(sqrt{n}) rounds for 6-cycle freeness cannot be improved using partition-based reductions from 2-party communication complexity, the technique by which all known lower bounds on subgraph detection have been proven to date. Second, we show that there is some fixed constant delta in (0,1/2) such that for any k, a Omega(n^{1/2+delta}) lower bound on C_{2k}-freeness implies new lower bounds in circuit complexity.For general subgraphs, it was shown in [Orr Fischer et al., 2018] that for any fixed k, there exists a subgraph H of size k such that H-freeness requires Omega~(n^{2-Theta(1/k)}) rounds. It was left as an open problem whether this is tight, or whether some constant-sized subgraph requires truly quadratic time to detect. We show that in fact, for any subgraph H of constant size k, the H-freeness problem can be solved in O(n^{2 - Theta(1/k)}) rounds, nearly matching the lower bound of [Orr Fischer et al., 2018].Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11322A Distributed Algorithm for Directed Minimum-Weight Spanning Tree
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11323
Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11323Stable Memoryless Queuing under Contention
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11324
Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11324Improved Network Decompositions Using Small Messages with Applications on MIS, Neighborhood Covers, and Beyond
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11325
Network decompositions, as introduced by Awerbuch, Luby, Goldberg, and Plotkin [FOCS'89], are one of the key algorithmic tools in distributed graph algorithms. We present an improved deterministic distributed algorithm for constructing network decompositions of power graphs using small messages, which improves upon the algorithm of Ghaffari and Kuhn [DISC'18]. In addition, we provide a randomized distributed network decomposition algorithm, based on our deterministic algorithm, with failure probability exponentially small in the input size that works with small messages as well. Compared to the previous algorithm of Elkin and Neiman [PODC'16], our algorithm achieves a better success probability at the expense of its round complexity, while giving a network decomposition of the same quality. As a consequence of the randomized algorithm for network decomposition, we get a faster randomized algorithm for computing a Maximal Independent Set, improving on a result of Ghaffari [SODA'19]. Other implications of our improved deterministic network decomposition algorithm are: a faster deterministic distributed algorithms for constructing spanners and approximations of distributed set cover, improving results of Ghaffari, and Kuhn [DISC'18] and Deurer, Kuhn, and Maus [PODC'19]; and faster a deterministic distributed algorithm for constructing neighborhood covers, resolving an open question of Elkin [SODA'04].Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11325On Bioelectric Algorithms
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11326
Cellular bioelectricity describes the biological phenomenon in which cells in living tissue generate and maintain patterns of voltage gradients across their membranes induced by differing concentrations of charged ions. A growing body of research suggests that bioelectric patterns represent an ancient system that plays a key role in guiding many important developmental processes including tissue regeneration, tumor suppression, and embryogenesis. This paper applies techniques from distributed algorithm theory to help better understand how cells work together to form these patterns. To do so, we present the cellular bioelectric model (CBM), a new computational model that captures the primary capabilities and constraints of bioelectric interactions between cells and their environment. We use this model to investigate several important topics from the relevant biology research literature. We begin with symmetry breaking, analyzing a simple cell definition that when combined in single hop or multihop topologies, efficiently solves leader election and the maximal independent set problem, respectively - indicating that these classical symmetry breaking tasks are well-matched to bioelectric mechanisms. We then turn our attention to the information processing ability of bioelectric cells, exploring upper and lower bounds for approximate solutions to threshold and majority detection, and then proving that these systems are in fact Turing complete - resolving an open question about the computational power of bioelectric interactions.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11326Parallel Finger Search Structures
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11327
In this paper we present two versions of a parallel finger structure FS on p processors that supports searches, insertions and deletions, and has a finger at each end. This is to our knowledge the first implementation of a parallel search structure that is work-optimal with respect to the finger bound and yet has very good parallelism (within a factor of O(log p)^2) of optimal). We utilize an extended implicit batching framework that transparently facilitates the use of FS by any parallel program P that is modelled by a dynamically generated DAG D where each node is either a unit-time instruction or a call to FS.The work done by FS is bounded by the finger bound F_L (for some linearization L of D), i.e. each operation on an item with distance r from a finger takes O(log r+1) amortized work. Running P using the simpler version takes O((T_1+F_L)/p + T_infty + d * ((log p)^2 + log n)) time on a greedy scheduler, where T_1, T_infty are the size and span of D respectively, and n is the maximum number of items in FS, and d is the maximum number of calls to FS along any path in D. Using the faster version, this is reduced to O((T_1+F_L)/p + T_infty + d *(log p)^2 + s_L) time, where s_L is the weighted span of D where each call to FS is weighted by its cost according to F_L. FS can be extended to a fixed number of movable fingers.The data structures in our paper fit into the dynamic multithreading paradigm, and their performance bounds are directly composable with other data structures given in the same paradigm. Also, the results can be translated to practical implementations using work-stealing schedulers.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11327Wait-Free Solvability of Equality Negation Tasks
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11328
We introduce a family of tasks for n processes, as a generalization of the two process equality negation task of Lo and Hadzilacos (SICOMP 2000). Each process starts the computation with a private input value taken from a finite set of possible inputs. After communicating with the other processes using immediate snapshots, the process must decide on a binary output value, 0 or 1. The specification of the task is the following: in an execution, if the set of input values is large enough, the processes should agree on the same output; if the set of inputs is small enough, the processes should disagree; and in-between these two cases, any output is allowed. Formally, this specification depends on two threshold parameters k and l, with k<l, indicating when the cardinality of the set of inputs becomes "small" or "large", respectively. We study the solvability of this task depending on those two parameters. First, we show that the task is solvable whenever k+2 <= l. For the remaining cases (l = k+1), we use various combinatorial topology techniques to obtain two impossibility results: the task is unsolvable if either k <= n/2 or n-k is odd. The remaining cases are still open.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11328Scalable Byzantine Reliable Broadcast
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11329
Byzantine reliable broadcast is a powerful primitive that allows a set of processes to agree on a message from a designated sender, even if some processes (including the sender) are Byzantine. Existing broadcast protocols for this setting scale poorly, as they typically build on quorum systems with strong intersection guarantees, which results in linear per-process communication and computation complexity.We generalize the Byzantine reliable broadcast abstraction to the probabilistic setting, allowing each of its properties to be violated with a fixed, arbitrarily small probability. We leverage these relaxed guarantees in a protocol where we replace quorums with stochastic samples. Compared to quorums, samples are significantly smaller in size, leading to a more scalable design. We obtain the first Byzantine reliable broadcast protocol with logarithmic per-process communication and computation complexity.We conduct a complete and thorough analysis of our protocol, deriving bounds on the probability of each of its properties being compromised. During our analysis, we introduce a novel general technique that we call adversary decorators. Adversary decorators allow us to make claims about the optimal strategy of the Byzantine adversary without imposing any additional assumptions. We also introduce Threshold Contagion, a model of message propagation through a system with Byzantine processes. To the best of our knowledge, this is the first formal analysis of a probabilistic broadcast protocol in the Byzantine fault model. We show numerically that practically negligible failure probabilities can be achieved with realistic security parameters.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11329Fast Distributed Algorithms for LP-Type Problems of Low Dimension
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11330
In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest enclosing ball and polytope distance, and set problems like hitting set and set cover. In the gossip model, a node can only push information to or pull information from nodes chosen uniformly at random. Protocols for the gossip model are usually very practical due to their fast convergence, their simplicity, and their stability under stress and disruptions. Our algorithms are very efficient (logarithmic rounds or better with just polylogarithmic communication work per node per round) whenever the combinatorial dimension of the given LP-type problem is constant, even if the size of the given LP-type problem is polynomially large in the number of nodes.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11330Privatization-Safe Transactional Memories
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11331
Transactional memory (TM) facilitates the development of concurrent applications by letting the programmer designate certain code blocks as atomic. Programmers using a TM often would like to access the same data both inside and outside transactions, and would prefer their programs to have a strongly atomic semantics, which allows transactions to be viewed as executing atomically with respect to non-transactional accesses. Since guaranteeing such semantics for arbitrary programs is prohibitively expensive, researchers have suggested guaranteeing it only for certain data-race free (DRF) programs, particularly those that follow the privatization idiom: from some point on, threads agree that a given object can be accessed non-transactionally.In this paper we show that a variant of Transactional DRF (TDRF) by Dalessandro et al. is appropriate for a class of privatization-safe TMs, which allow using privatization idioms. We prove that, if such a TM satisfies a condition we call privatization-safe opacity and a program using the TM is TDRF under strongly atomic semantics, then the program indeed has such semantics. We also present a method for proving privatization-safe opacity that reduces proving this generalization to proving the usual opacity, and apply the method to a TM based on two-phase locking and a privatization-safe version of TL2. Finally, we establish the inherent cost of privatization-safety: we prove that a TM cannot be progressive and have invisible reads if it guarantees strongly atomic semantics for TDRF programs.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11331Low-Congestion Shortcut and Graph Parameters
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11332
Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Omega~(sqrt{n} + D) rounds for many global problems, where n is the number of nodes and D is the diameter of the input graph. Since such a lower bound is derived from special "hard-core" instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts is initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. Specifically, given a specific graph class X, an f-round algorithm of constructing shortcuts of quality q for any instance in X results in O~(q + f)-round algorithms of solving several fundamental graph problems such as minimum spanning tree and minimum cut, for X. The main interest on this line is to identify the graph classes allowing the shortcuts which are efficient in the sense of breaking O~(sqrt{n}+D)-round general lower bounds.In this paper, we consider the relationship between the quality of low-congestion shortcuts and three major graph parameters, chordality, diameter, and clique-width. The main contribution of the paper is threefold: (1) We show an O(1)-round algorithm which constructs a low-congestion shortcut with quality O(kD) for any k-chordal graph, and prove that the quality and running time of this construction is nearly optimal up to polylogarithmic factors. (2) We present two algorithms, each of which constructs a low-congestion shortcut with quality O~(n^{1/4}) in O~(n^{1/4}) rounds for graphs of D=3, and that with quality O~(n^{1/3}) in O~(n^{1/3}) rounds for graphs of D=4 respectively. These results obviously deduce two MST algorithms running in O~(n^{1/4}) and O~(n^{1/3}) rounds for D=3 and 4 respectively, which almost close the long-standing complexity gap of the MST construction in small-diameter graphs originally posed by Lotker et al. [Distributed Computing 2006]. (3) We show that bounding clique-width does not help the construction of good shortcuts by presenting a network topology of clique-width six where the construction of MST is as expensive as the general case.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11332The Complexity of Symmetry Breaking in Massive Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11333
The goal of this paper is to understand the complexity of symmetry breaking problems, specifically maximal independent set (MIS) and the closely related beta-ruling set problem, in two computational models suited for large-scale graph processing, namely the k-machine model and the graph streaming model. We present a number of results. For MIS in the k-machine model, we improve the O~(m/k^2 + Delta/k)-round upper bound of Klauck et al. (SODA 2015) by presenting an O~(m/k^2)-round algorithm. We also present an Omega~(n/k^2) round lower bound for MIS, the first lower bound for a symmetry breaking problem in the k-machine model. For beta-ruling sets, we use hierarchical sampling to obtain more efficient algorithms in the k-machine model and also in the graph streaming model. More specifically, we obtain a k-machine algorithm that runs in O~(beta n Delta^{1/beta}/k^2) rounds and, by using a similar hierarchical sampling technique, we obtain one-pass algorithms for both insertion-only and insertion-deletion streams that use O(beta * n^{1+1/2^{beta-1}}) space. The latter result establishes a clear separation between MIS, which is known to require Omega(n^2) space (Cormode et al., ICALP 2019), and beta-ruling sets, even for beta = 2. Finally, we present an even faster 2-ruling set algorithm in the k-machine model, one that runs in O~(n/k^{2-epsilon} + k^{1-epsilon}) rounds for any epsilon, 0 <=epsilon <=1. For a wide range of values of k this round complexity simplifies to O~(n/k^2) rounds, which we conjecture is optimal.Our results use a variety of techniques. For our upper bounds, we prove and use simulation theorems for beeping algorithms, hierarchical sampling, and L_0-sampling, whereas for our lower bounds we use information-theoretic arguments and reductions to 2-party communication complexity problems.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11333Stellar Consensus by Instantiation
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11334
Stellar introduced a new type of quorum system called a Federated Byzantine Agreement System. A major difference between this novel type of quorum system and a threshold quorum system is that each participant has its own, personal notion of a quorum. Thus, unlike in a traditional BFT system, designed for a uniform notion of quorum, even in a time of synchrony one well-behaved participant may observe a quorum of well-behaved participants, while others may not. To tackle this new problem in a more general setting, we abstract the Stellar Network as an instance of what we call Personal Byzantine Quorum Systems. Using this notion, we streamline the theory behind the Stellar Network, removing the clutter of unnecessary details, and refute the conjecture that Stellar's notion of intact set is optimally fault-tolerant. Most importantly, we develop a new consensus algorithm for the new setting.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11334A Scalable, Portable, and Memory-Efficient Lock-Free FIFO Queue
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11335
We present a new lock-free multiple-producer and multiple-consumer (MPMC) FIFO queue design which is scalable and, unlike existing high-performant queues, very memory efficient. Moreover, the design is ABA safe and does not require any external memory allocators or safe memory reclamation techniques, typically needed by other scalable designs. In fact, this queue itself can be leveraged for object allocation and reclamation, as in data pools. We use FAA (fetch-and-add), a specialized and more scalable than CAS (compare-and-set) instruction, on the most contended hot spots of the algorithm. However, unlike prior attempts with FAA, our queue is both lock-free and linearizable.We propose a general approach, SCQ, for bounded queues. This approach can easily be extended to support unbounded FIFO queues which can store an arbitrary number of elements. SCQ is portable across virtually all existing architectures and flexible enough for a wide variety of uses. We measure the performance of our algorithm on the x86-64 and PowerPC architectures. Our evaluation validates that our queue has exceptional memory efficiency compared to other algorithms and its performance is often comparable to, or exceeding that of state-of-the-art scalable algorithms.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11335Byzantine Approximate Agreement on Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11336
Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that 1) the output values are in the convex hull of the non-faulty processors' input values, 2) the output values are within distance d of each other. Classically, the values are assumed to be from an m-dimensional Euclidean space, where m >= 1.In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d=0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d >= 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (omega+1)f, where omega is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11336Small Cuts and Connectivity Certificates: A Fault Tolerant Approach
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11337
We revisit classical connectivity problems in the {CONGEST} model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with O~(1) rounds) for problems that are closely related to hard global problems (i.e., with a lower bound of Omega(Diam+sqrt{n}) rounds).Distributed Minimum Cut: Nanongkai and Su presented a randomized algorithm for computing a (1+epsilon)-approximation of the minimum cut using O~(D +sqrt{n}) rounds where D is the diameter of the graph. For a sufficiently large minimum cut lambda=Omega(sqrt{n}), this is tight due to Das Sarma et al. [FOCS '11], Ghaffari and Kuhn [DISC '13]. - Small Cuts: A special setting that remains open is where the graph connectivity lambda is small (i.e., constant). The only lower bound for this case is Omega(D), with a matching bound known only for lambda <= 2 due to Pritchard and Thurimella [TALG '11]. Recently, Daga, Henzinger, Nanongkai and Saranurak [STOC '19] raised the open problem of computing the minimum cut in poly(D) rounds for any lambda=O(1). In this paper, we resolve this problem by presenting a surprisingly simple algorithm, that takes a completely different approach than the existing algorithms. Our algorithm has also the benefit that it computes all minimum cuts in the graph, and naturally extends to vertex cuts as well. At the heart of the algorithm is a graph sampling approach usually used in the context of fault tolerant (FT) design. - Deterministic Algorithms: While the existing distributed minimum cut algorithms are randomized, our algorithm can be made deterministic within the same round complexity. To obtain this, we introduce a novel definition of universal sets along with their efficient computation. This allows us to derandomize the FT graph sampling technique, which might be of independent interest. - Computation of all Edge Connectivities: We also consider the more general task of computing the edge connectivity of all the edges in the graph. In the output format, it is required that the endpoints u,v of every edge (u,v) learn the cardinality of the u-v cut in the graph. We provide the first sublinear algorithm for this problem for the case of constant connectivity values. Specifically, by using the recent notion of low-congestion cycle cover, combined with the sampling technique, we compute all edge connectivities in poly(D) * 2^{O(sqrt{log n log log n})} rounds. Sparse Certificates: For an n-vertex graph G and an integer lambda, a lambda-sparse certificate H is a subgraph H subseteq G with O(lambda n) edges which is lambda-connected iff G is lambda-connected. For D-diameter graphs, constructions of sparse certificates for lambda in {2,3} have been provided by Thurimella [J. Alg. '97] and Dori [PODC '18] respectively using O~(D) number of rounds. The problem of devising such certificates with o(D+sqrt{n}) rounds was left open by Dori [PODC '18] for any lambda >= 4. Using connections to fault tolerant spanners, we considerably improve the round complexity for any lambda in [1,n] and epsilon in (0,1), by showing a construction of (1-epsilon)lambda-sparse certificates with O(lambda n) edges using only O(1/epsilon^2 * log^{2+o(1)} n) rounds.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11337Monotonically Relaxing Concurrent Data-Structure Semantics for Increasing Performance: An Efficient 2D Design Framework
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11338
There has been a significant amount of work in the literature proposing semantic relaxation of concurrent data structures for improving scalability and performance. By relaxing the semantics of a data structure, a bigger design space, that allows weaker synchronization and more useful parallelism, is unveiled. Investigating new data structure designs, capable of trading semantics for achieving better performance in a monotonic way, is a major challenge in the area. We algorithmically address this challenge in this paper.We present an efficient, lock-free, concurrent data structure design framework for out-of-order semantic relaxation. We introduce a new two dimensional algorithmic design, that uses multiple instances of a given data structure. The first dimension of our design is the number of data structure instances operations are spread to, in order to benefit from parallelism through disjoint memory access; the second dimension is the number of consecutive operations that try to use the same data structure instance in order to benefit from data locality. Our design can flexibly explore this two-dimensional space to achieve the property of monotonically relaxing concurrent data structure semantics for better performance within a tight deterministic relaxation bound, as we prove in the paper.We show how our framework can instantiate lock-free out-of-order queues, stacks, counters and dequeues. We provide implementations of these relaxed data structures and evaluate their performance and behaviour on two parallel architectures. Experimental evaluation shows that our two-dimensional design significantly outperforms the respected previous proposed designs with respect to scalability and performance. Moreover, our design increases performance monotonically as relaxation increases.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11338Phase Transitions of Best-of-Two and Best-of-Three on Stochastic Block Models
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11339
Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11339Distributed Data Summarization in Well-Connected Networks
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11340
We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph G of n nodes each of which may hold a value initially, we focus on computing sum_{i=1}^N g(f_i), where f_i is the number of occurrences of value i and g is some fixed function. This includes important statistics such as the number of distinct elements, frequency moments, and the empirical entropy of the data. In the CONGEST~ model, a simple adaptation from streaming lower bounds shows that it requires Omega~(D+ n) rounds, where D is the diameter of the graph, to compute some of these statistics exactly. However, these lower bounds do not hold for graphs that are well-connected. We give an algorithm that computes sum_{i=1}^{N} g(f_i) exactly in {tau_{G}} * 2^{O(sqrt{log n})} rounds where {tau_{G}} is the mixing time of G. This also has applications in computing the top k most frequent elements.We demonstrate that there is a high similarity between the GOSSIP~ model and the CONGEST~ model in well-connected graphs. In particular, we show that each round of the GOSSIP~ model can be simulated almost perfectly in O~({tau_{G}}) rounds of the CONGEST~ model. To this end, we develop a new algorithm for the GOSSIP~ model that 1 +/- epsilon approximates the p-th frequency moment F_p = sum_{i=1}^N f_i^p in O~(epsilon^{-2} n^{1-k/p}) rounds , for p >= 2, when the number of distinct elements F_0 is at most O(n^{1/(k-1)}). This result can be translated back to the CONGEST~ model with a factor O~({tau_{G}}) blow-up in the number of rounds.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11340Polynomial-Time Fence Insertion for Structured Programs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11341
To enhance performance, common processors feature relaxed memory models that reorder instructions. However, the correctness of concurrent programs is often dependent on the preservation of the program order of certain instructions. Thus, the instruction set architectures offer memory fences. Using fences is a subtle task with performance and correctness implications: using too few can compromise correctness and using too many can hinder performance. Thus, fence insertion algorithms that given the required program orders can automatically find the optimum fencing can enhance the ease of programming, reliability, and performance of concurrent programs. In this paper, we consider the class of programs with structured branch and loop statements and present a greedy and polynomial-time optimum fence insertion algorithm. The algorithm incrementally reduces fence insertion for a control-flow graph to fence insertion for a set of paths. In addition, we show that the minimum fence insertion problem with multiple types of fence instructions is NP-hard even for straight-line programs.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11341Brief Announcement: On Self-Adjusting Skip List Networks
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11342
This paper explores the design of dynamic network topologies which adjust to the workload they serve, in an online manner. Such self-adjusting networks (SANs) are enabled by emerging optical technologies, and can be found, e.g., in datacenters. SANs can be used to reduce routing costs by moving frequently communicating nodes topologically closer. This paper presents SANs which provide, for the first time, provable working set guarantees: the routing cost between node pairs is proportional to how recently these nodes communicated last time. Our SANs rely on skip lists (which serve as the topology) and provide additional interesting properties such as local routing.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11342Brief Announcement: Streaming and Massively Parallel Algorithms for Edge Coloring
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11343
A valid edge-coloring of a graph is an assignment of "colors" to its edges such that no two incident edges receive the same color. The goal is to find a proper coloring that uses few colors. In this paper, we revisit this problem in two models of computation specific to massive graphs, the Massively Parallel Computations (MPC) model and the Graph Streaming model: Massively Parallel Computation. We give a randomized MPC algorithm that w.h.p., returns a (1+o(1))Delta edge coloring in O(1) rounds using O~(n) space per machine and O(m) total space. The space per machine can also be further improved to n^{1-Omega(1)} if Delta = n^{Omega(1)}. This is, to our knowledge, the first constant round algorithm for a natural graph problem in the strongly sublinear regime of MPC. Our algorithm improves a previous result of Harvey et al. [SPAA 2018] which required n^{1+Omega(1)} space to achieve the same result. Graph Streaming. Since the output of edge-coloring is as large as its input, we consider a standard variant of the streaming model where the output is also reported in a streaming fashion. The main challenge is that the algorithm cannot "remember" all the reported edge colors, yet has to output a proper edge coloring using few colors.We give a one-pass O~(n)-space streaming algorithm that always returns a valid coloring and uses 5.44 Delta colors w.h.p., if the edges arrive in a random order. For adversarial order streams, we give another one-pass O~(n)-space algorithm that requires O(Delta^2) colors.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11343Brief Announcement: Memory Lower Bounds for Self-Stabilization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11344
In the context of self-stabilization, a silent algorithm guarantees that the communication registers (a.k.a register) of every node do not change once the algorithm has stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent deterministic algorithm must use a memory of Omega(log n) bits per register in n-node networks. Similarly, Korman et al. [Dist. Comp. '07] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning tree (MST), every silent algorithm must use a memory of Omega(log^2n) bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity.In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary deterministic self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for deterministic general algorithms, also established at the end of the 90's, is due to Beauquier et al. [PODC '99] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing the lower bound Omega(log log n) bits per register for deterministic self-stabilizing algorithms solving (Delta+1)-coloring, leader election or constructing a spanning tree in networks of maximum degree Delta.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11344Brief Announcement: Wait-Free Universality of Consensus in the Infinite Arrival Model
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11345
In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been proved that consensus is universal in such systems, which means that this system augmented with consensus objects allows to implement any object that has a sequential specification. In this paper, we consider a more general system model called infinite arrival model where infinitely many processes may arrive and leave or crash during a run. We prove that consensus is still universal in this more general model. For that, we propose a universal construction based on a weak log that can be implementated using consensus objects.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11345Brief Announcement: Asymmetric Distributed Trust
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11346
Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory and broadcast primitives with processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11346Brief Announcement: Implementing Byzantine Tolerant Distributed Ledger Objects
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11347
Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11347Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11348
This announces the first successful attempt at using model-checking techniques to verify the correctness of self-stabilizing distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights and presents a generic verification model for the SPIN model checker. It will be presented in full at an upcoming venue.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11348Brief Announcement: Massively Parallel Approximate Distance Sketches
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11349
Data structures that allow efficient distance estimation have been extensively studied both in centralized models and classical distributed models. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm that constructs distance sketches with worse stretch but that only takes polylogarithmic rounds. Along the way, we show that other useful combinatorial structures can also be computed in MPC. In particular, one key component we use is an MPC construction of the hopsets of Elkin and Neiman (2016). This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11349Brief Announcement: Neighborhood Mutual Remainder and Its Self-Stabilizing Implementation of Look-Compute-Move Robots
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11350
In this paper, we define a new concept neighborhood mutual remainder (NMR). An NMR distributed algorithms should satisfy global fairness, l-exclusion and repeated local rendezvous requirements. We give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve NMR, and also present applications of NMR to a Look-Compute-Move robot system.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11350Brief Announcement: Revisiting Consensus Protocols through Wait-Free Parallelization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11351
In this brief announcement, we propose a protocol-agnostic approach to improve the design of primary-backup consensus protocols. At the core of our approach is a novel wait-free design of running several instances of the underlying consensus protocol in parallel. To yield a high-performance parallelized design, we present coordination-free techniques to order operations across parallel instances, deal with instance failures, and assign clients to specific instances. Consequently, the design we present is able to reduce the load on individual instances and primaries, while also reducing the adverse effects of any malicious replicas. Our design is fine-tuned such that the instances coordinated by non-faulty replicas are wait-free: they can continuously make consensus decisions, independent of the behavior of any other instances.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11351Brief Announcement: The Fault-Tolerant Cluster-Sending Problem
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11352
The development of fault-tolerant distributed systems that can tolerate Byzantine behavior has traditionally been focused on consensus protocols, which support fully-replicated designs. For the development of more sophisticated high-performance Byzantine distributed systems, more specialized fault-tolerant communication primitives are necessary, however.In this brief announcement, we identify the cluster-sending problem - the problem of sending a message from one Byzantine cluster to another Byzantine cluster in a reliable manner - as such an essential communication primitive. We not only formalize this fundamental problem, but also establish lower bounds on the complexity of this problem under crash failures and Byzantine failures. Furthermore, we develop practical cluster-sending protocols that meet these lower bounds and, hence, have optimal complexity. As such, our work provides a strong foundation for the further exploration of novel designs that address challenges encountered in fault-tolerant distributed systems.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11352Brief Announcement: On the Correctness of Transaction Processing with External Dependency
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11353
We briefly introduce a unified model to characterize correctness levels stronger (or equal to) serializability in the presence of application invariant. We propose to classify relations among committed transactions into data-related and application semantic-related. Our model delivers a condition that can be used to verify the safety of transactional executions in the presence of application invariant.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11353Brief Announcement: Towards Byzantine Broadcast in Generalized Communication and Adversarial Models
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11354
Byzantine broadcast is a primitive which allows a specific party to distribute a message consistently among n parties, even if up to t parties exhibit malicious behaviour. In the classical model with a complete network of bilateral authenticated channels, the seminal result of Pease et al. [Pease et al., 1980] shows that broadcast is achievable if and only if t < n/3. There are two generalizations suggested for the broadcast problem - w.r.t. the adversarial model and the communication model. Fitzi and Maurer [Fitzi and Maurer, 1998] consider a (non-threshold) general adversary that is characterized by the subsets of parties that could be corrupted, and show that broadcast can be realized from bilateral channels if and only if the union of no three possible corrupted sets equals the entire set of n parties. On the other hand, Considine et al. [Considine et al., 2005] extend the standard model of bilateral channels with the existence of b-minicast channels that allow to locally broadcast among any subset of b parties; the authors show that in this enhanced model of communication, secure broadcast tolerating up to t corrupted parties is possible if and only if t < (b-1)/(b+1) n. These generalizations are unified in the work by Raykov [Raykov P., 2015], where a tight condition on the possible corrupted sets such that broadcast is achievable from a complete set of b-minicasts is shown. This paper investigates the achievability of broadcast in general networks, i.e., networks where only some subsets of minicast channels may be available, thereby addressing open problems posed in [Jaffe et al., 2012; Raykov P., 2015]. Our contributions include: 1) proposing a hierarchy over all possible general adversaries for a clean analysis of the broadcast problem in general networks, 2) showing the infeasibility of a prominent technique - used to achieve broadcast in general 3-minicast networks [Ravikant et al., 2004] - with regard to higher b-minicast networks, and 3) providing some necessary conditions on general networks for broadcast to be possible while tolerating general adversaries.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11354Brief Announcement: Integrating Temporal Information to Spatial Information in a Neural Circuit
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11355
In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems: "First Consecutive Spikes Counting" and "Total Spikes Counting", which model temporal-coding and rate-coding aspects of temporal-to-spatial translation respectively. Assuming an upper bound of T on the length of the temporal input signal, we design two networks that solve two problems, each using O(log T) neurons and terminating in time T+1. We also prove that these bounds are tight.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11355Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11356
Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost. The first work to succeed in computing a spanning tree with communication sublinear in the number of edges in an asynchronous CONGEST network appeared in DISC 2018. That algorithm which constructs an MST is sequential in the worst case; its running time is proportional to the total number of messages sent. Our paper matches its message complexity but brings the running time down to linear in n. Our techniques can also be used to provide an asynchronous algorithm with sublinear communication to construct a tree in which the distance from a source to each node is within an additive term of sqrt{n} of its actual distance.Fri, 11 Oct 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11356Multi-Document Information Consolidation (Dagstuhl Seminar 19182)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11357
This report documents the program and the outcomes of Dagstuhl Seminar 19182 "Multi-Document Information Consolidation". At this 5-day Dagstuhl seminar, an interdisciplinary collection of leading researchers discussed and develop research ideas to address multi-documents in machine learning and NLP systems. In particular, the seminar addressed four major topics: 1) how to represent information in multi-document repositories; 2) how to support inference over multi-document repositories; 3) how to summarize and visualize multi-document repositories for decision support; and 4) how to do information validation on multi-document repositories. General talks as well as topic-specific talks were given to stimulate the discussion between the participants, which lead to various new research ideas.Mon, 30 Sep 2019 09:58:27 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11357Computational Geometry (Dagstuhl Seminar 19181)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11306
This report documents the program and the outcomes of Dagstuhl Seminar 19181 "Computational Geometry". The seminar was held from April 28 to May 3, 2019 and 40 participants from various countries attended it. New advances and directions in computational geometry were presented and discussed. The report collects the abstracts of talks and open problems presented in the seminar.Mon, 30 Sep 2019 09:58:15 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11306Computational Creativity Meets Digital Literary Studies (Dagstuhl Seminar 19172)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11305
This report documents the outcomes of Dagstuhl Seminar 19172 "Computational Creativity Meets Digital Literary Studies", held from April 22 to April 25, 2019. Computational Creativity and Digital Humanities are emerging, interdisciplinary fields still experiencing significant growth and development in terms of community, research questions, methods, and approaches. Computational Storytelling as a prominent subfield within Computational Creativity that has mostly focused on planning stories - thus simulating a logically coherent plot - could fruitfully extend its horizon to narrative concepts like narrative style, chronology of narratives, focalization and perspective. These narratological concepts have been investigated by literary scholars for a long time. Yet, operationalization of these concepts is required when used as the basis for computational modelling. This in turn sharpens the definitions of theoretical considerations and can feed back into theoretical discussions in the literary studies. Moreover, there are obvious connection points between Computational Creativity and Natural Language Processing on the one hand, and between Natural Language Processing and Digital Literary Studies on the other hand. However, these connections currently are not transitive. The goal of the seminar was to establish international links between all three disciplines and among involved researchers through presentations by participants and extensive group-work sessions.Mon, 30 Sep 2019 09:58:04 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11305Ethics and Trust: Principles, Verification and Validation (Dagstuhl Seminar 19171)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11304
This report documents the programme of, and outcomes from, the Dagstuhl Seminar 19171 on "Ethics and Trust: Principles, Verification and Validation". We consider the issues of ethics and trust as crucial to the future acceptance and use of autonomous systems. The development of new classes of autonomous systems, such as medical robots, "driver-less" cars, and assistive care robots has opened up questions on how we can integrate truly autonomous systems into our society. Once a system is truly autonomous, i.e. learning from interactions, moving and manipulating the world we are living in, and making decisions by itself, we must be certain that it will act in a safe and ethical way, i.e. that it will be able to distinguish 'right' from `wrong' and make the decisions we would expect of it. In order for society to accept these new machines, we must also trust them, i.e. we must believe that they are reliable and that they are trying to assist us, especially when engaged in close human-robot interaction. The seminar focused on questions of how does trust with autonomous machines evolve, how to build a `practical' ethical and trustworthy system, and what are the societal implications. Key issues included: Change of trust and trust repair, AI systems as decision makers, complex system of norms and algorithmic bias, and potential discrepancies between expectations and capabilities of autonomous machines.This workshop was a follow-up to the 2016 Dagstuhl Seminar 16222 on Engineering Moral Agents: From Human Morality to Artificial Morality. When organizing this workshop we aimed to bring together communities of researchers from moral philosophy and from artificial intelligence and extend it with researchers from (social) robotics and human-robot interaction research.Mon, 30 Sep 2019 09:57:49 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11304Emerging Hardware Techniques and EDA Methodologies for Neuromorphic Computing (Dagstuhl Seminar 19152)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11303
Mon, 30 Sep 2019 09:57:31 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11303Visual Computing in Materials Sciences (Dagstuhl Seminar 19151)
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11302
Visual computing has become highly attractive for boosting research endeavors in the materials science domain. Using visual computing, a multitude of different phenomena may now be studied, at various scales, dimensions, or using different modalities. This was simply impossible before. Visual computing techniques generate novel insights to understand, discover, design, and use complex material systems of interest. Its huge potential for retrieving and visualizing (new) information on materials, their characteristics and interrelations as well as on simulating the material's behavior in its target application environment is of core relevance to material scientists. This Dagstuhl seminar on Visual Computing in Materials Sciences thus focuses on the intersection of both domains to guide research endeavors in this field. It targets to provide answers regarding the following four challenges, which are of imminent need:-The Integrated Visual Analysis Challeng identifies standard visualization tools as insufficient for exploring materials science data in detail. What is required are integrated visual analysis tools, which are tailored to a specific application area and guide users in their investigations. Using linked views and other interaction concepts, these tools are required to combine all data domains using meaningful and easy to understand visualization techniques. Especially for the analysis of spatial and temporal data in dynamic processes (e.g., materials tested under load or in different environmental conditions) or multimodal, multiscale data, these tools and techniques are highly anticipated. Only integrated analysis concepts allow to make the most out of all the data available.- The Quantitative Data Visualization Challenge centers around the design and implementation of tailored visual analysis systems for extracting and analyzing derived data (e.g., computed from extracted features over spatial, temporal or even higher dimensional domains). Therefore, feature extraction and quantification techniques, segmentation techniques, or clustering techniques, are required as prerequisites for the targeted visual analysis. As the quantification may easily end up in 25 or more properties to be computed per feature, clustering techniques allow to distinguish features of interest into feature classes. These feature classes may then be statistically evaluated to visualize the properties of the individual features as well as the properties of the different classes. Information visualization techniques will be of special interest for solving this challenge.- The Visual Debugger Challenge is an idea which uses visual analysis to remove errors in the parametrization of a simulation or a data acquisition process. Similarly, to a debugger in computer programming, identifying errors in the code and providing hints to improve, a visual debugger in the domain of visual computing for materials science should show the following characteristics: It should indicate errors and identify wrongly used algorithms in the data analysis. Such a tool should also identify incorrect parameters, which either show no or very limited benefit or even provide erroneous results. Furthermore, it should give directions on how to improve a targeted analysis and suggest suitable algorithms or pipelines for specific tasks.- The Interactive Steering Challenge uses visual analysis tools to control a running simulation or an ongoing data acquisition process. Respective tools monitor costly processes and give directions to improve results regarding the respective targets. For example, in the material analysis domain, this could be a system which provides settings for improved data acquisition based on the current image quality achieved: If the image quality does no more fulfill the target requirements, the system influences all degrees of freedom in the data acquisition to enhance image quality. The same holds for the materials simulation domain. Visual analysis can help to steer target material properties in a specific application environment by predicting tendencies of costly simulation runs, e.g., using cheaper surrogate models.Mon, 30 Sep 2019 09:56:56 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11302LIPIcs, Volume 145, APPROX/RANDOM'19, Complete Volume
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11301
LIPIcs, Volume 145, APPROX/RANDOM'19, Complete VolumeWed, 25 Sep 2019 10:21:15 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11301Front Matter, Table of Contents, Preface, Conference Organization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11215
Front Matter, Table of Contents, Preface, Conference OrganizationThu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11215The Query Complexity of Mastermind with l_p Distances
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11216
Consider a variant of the Mastermind game in which queries are l_p distances, rather than the usual Hamming distance. That is, a codemaker chooses a hidden vector y in {-k,-k+1,...,k-1,k}^n and answers to queries of the form ||y-x||_p where x in {-k,-k+1,...,k-1,k}^n. The goal is to minimize the number of queries made in order to correctly guess y.In this work, we show an upper bound of O(min{n,(n log k)/(log n)}) queries for any real 1<=p<infty and O(n) queries for p=infty. To prove this result, we in fact develop a nonadaptive polynomial time algorithm that works for a natural class of separable distance measures, i.e., coordinate-wise sums of functions of the absolute value. We also show matching lower bounds up to constant factors, even for adaptive algorithms for the approximation version of the problem, in which the problem is to output y' such that ||y'-y||_p <= R for any R <= k^{1-epsilon}n^{1/p} for constant epsilon>0. Thus, essentially any approximation of this problem is as hard as finding the hidden vector exactly, up to constant factors. Finally, we show that for the noisy version of the problem, i.e., the setting when the codemaker answers queries with any q = (1 +/- epsilon)||y-x||_p, there is no query efficient algorithm.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11216Tracking the l_2 Norm with Constant Update Time
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11217
The l_2 tracking problem is the task of obtaining a streaming algorithm that, given access to a stream of items a_1,a_2,a_3,... from a universe [n], outputs at each time t an estimate to the l_2 norm of the frequency vector f^{(t)}in R^n (where f^{(t)}_i is the number of occurrences of item i in the stream up to time t). The previous work [Braverman-Chestnut-Ivkin-Nelson-Wang-Woodruff, PODS 2017] gave a streaming algorithm with (the optimal) space using O(epsilon^{-2}log(1/delta)) words and O(epsilon^{-2}log(1/delta)) update time to obtain an epsilon-accurate estimate with probability at least 1-delta. We give the first algorithm that achieves update time of O(log 1/delta) which is independent of the accuracy parameter epsilon, together with the nearly optimal space using O(epsilon^{-2}log(1/delta)) words. Our algorithm is obtained using the Count Sketch of [Charilkar-Chen-Farach-Colton, ICALP 2002].Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11217Submodular Optimization with Contention Resolution Extensions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11218
This paper considers optimizing a submodular function subject to a set of downward closed constraints. Previous literature on this problem has often constructed solutions by (1) discovering a fractional solution to the multi-linear extension and (2) rounding this solution to an integral solution via a contention resolution scheme. This line of research has improved results by either optimizing (1) or (2).Diverging from previous work, this paper introduces a principled method called contention resolution extensions of submodular functions. A contention resolution extension combines the contention resolution scheme into a continuous extension of a discrete submodular function. The contention resolution extension can be defined from effectively any contention resolution scheme. In the case where there is a loss in both (1) and (2), by optimizing them together, the losses can be combined resulting in an overall improvement. This paper showcases the concept by demonstrating that for the problem of optimizing a non-monotone submodular subject to the elements forming an independent set in an interval graph, the algorithm gives a .188-approximation. This improves upon the best known 1/(2e)~eq .1839 approximation.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11218Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11219
In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may build rigid resources that cannot be changed for different scenarios. Once we know which scenarios appear, we are allowed to rent reconfigurable but expensive resources to use across scenarios. Although computing the objective in our model might seem to require enumerating exponentially-many possibilities, we show it is well estimated by a surrogate objective which is representable by a polynomial-size LP. In this surrogate objective we pay for each scenario only to the extent that it exceeds a certain threshold. Using this objective we design algorithms that approximately-optimally balance inflexible and reconfigurable resources for several NP-hard covering problems. For example, we study variants of minimum spanning and Steiner trees, minimum cuts, and facility location. Up to constants, our approximation guarantees match those of previously-studied algorithms for demand-robust and stochastic two-stage models. Lastly, we demonstrate that our problem is sufficiently general to smoothly interpolate between previous demand-robust and stochastic two-stage problems.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11219Streaming Hardness of Unique Games
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11220
We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by p, the alphabet size of the Unique Game, gives a trivial p-approximation that can be computed in O(log n) space. Meanwhile, with high probability, a sample of O~(n) constraints suffices to estimate the optimal value to (1+epsilon) accuracy. We prove that any single-pass streaming algorithm that achieves a (p-epsilon)-approximation requires Omega_epsilon(sqrt n) space. Our proof is via a reduction from lower bounds for a communication problem that is a p-ary variant of the Boolean Hidden Matching problem studied in the literature. Given the utility of Unique Games as a starting point for reduction to other optimization problems, our strong hardness for approximating Unique Games could lead to downstream hardness results for streaming approximability for other CSP-like problems.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11220On Strong Diameter Padded Decompositions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11221
Given a weighted graph G=(V,E,w), a partition of V is Delta-bounded if the diameter of each cluster is bounded by Delta. A distribution over Delta-bounded partitions is a beta-padded decomposition if every ball of radius gamma Delta is contained in a single cluster with probability at least e^{-beta * gamma}. The weak diameter of a cluster C is measured w.r.t. distances in G, while the strong diameter is measured w.r.t. distances in the induced graph G[C]. The decomposition is weak/strong according to the diameter guarantee.Formerly, it was proven that K_r free graphs admit weak decompositions with padding parameter O(r), while for strong decompositions only O(r^2) padding parameter was known. Furthermore, for the case of a graph G, for which the induced shortest path metric d_G has doubling dimension ddim, a weak O(ddim)-padded decomposition was constructed, which is also known to be tight. For the case of strong diameter, nothing was known.We construct strong O(r)-padded decompositions for K_r free graphs, matching the state of the art for weak decompositions. Similarly, for graphs with doubling dimension ddim we construct a strong O(ddim)-padded decomposition, which is also tight. We use this decomposition to construct (O(ddim),O~(ddim))-sparse cover scheme for such graphs. Our new decompositions and cover have implications to approximating unique games, the construction of light and sparse spanners, and for path reporting distance oracles.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11221Max-Min Greedy Matching
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11222
A bipartite graph G(U,V;E) that admits a perfect matching is given. One player imposes a permutation pi over V, the other player imposes a permutation sigma over U. In the greedy matching algorithm, vertices of U arrive in order sigma and each vertex is matched to the highest (under pi) yet unmatched neighbor in V (or left unmatched, if all its neighbors are already matched). The obtained matching is maximal, thus matches at least a half of the vertices. The max-min greedy matching problem asks: suppose the first (max) player reveals pi, and the second (min) player responds with the worst possible sigma for pi, does there exist a permutation pi ensuring to match strictly more than a half of the vertices? Can such a permutation be computed in polynomial time?The main result of this paper is an affirmative answer for these questions: we show that there exists a polytime algorithm to compute pi for which for every sigma at least rho > 0.51 fraction of the vertices of V are matched. We provide additional lower and upper bounds for special families of graphs, including regular and Hamiltonian graphs. Our solution solves an open problem regarding the welfare guarantees attainable by pricing in sequential markets with binary unit-demand valuations.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11222Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11223
We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11223Improved 3LIN Hardness via Linear Label Cover
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11224
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11224Dynamic Pricing of Servers on Trees
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11225
In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server.This paper extends [Ilan Reuven Cohen et al., 2015], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an alpha-competitive dynamic pricing scheme exists on the tree if and only if there exists alpha-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11225Approximating the Norms of Graph Spanners
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Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11226Conditional Hardness of Earth Mover Distance
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11227
The Earth Mover Distance (EMD) between two sets of points A, B subseteq R^d with |A| = |B| is the minimum total Euclidean distance of any perfect matching between A and B. One of its generalizations is asymmetric EMD, which is the minimum total Euclidean distance of any matching of size |A| between sets of points A,B subseteq R^d with |A| <= |B|. The problems of computing EMD and asymmetric EMD are well-studied and have many applications in computer science, some of which also ask for the EMD-optimal matching itself. Unfortunately, all known algorithms require at least quadratic time to compute EMD exactly. Approximation algorithms with nearly linear time complexity in n are known (even for finding approximately optimal matchings), but suffer from exponential dependence on the dimension.In this paper we show that significant improvements in exact and approximate algorithms for EMD would contradict conjectures in fine-grained complexity. In particular, we prove the following results: - Under the Orthogonal Vectors Conjecture, there is some c>0 such that EMD in Omega(c^{log^* n}) dimensions cannot be computed in truly subquadratic time. - Under the Hitting Set Conjecture, for every delta>0, no truly subquadratic time algorithm can find a (1 + 1/n^delta)-approximate EMD matching in omega(log n) dimensions. - Under the Hitting Set Conjecture, for every eta = 1/omega(log n), no truly subquadratic time algorithm can find a (1 + eta)-approximate asymmetric EMD matching in omega(log n) dimensions.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11227Single-Elimination Brackets Fail to Approximate Copeland Winner
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11228
Single-elimination (SE) brackets appear commonly in both sports tournaments and the voting theory literature. In certain tournament models, they have been shown to select the unambiguously-strongest competitor with optimum probability. By contrast, we reevaluate SE brackets through the lens of approximation, where the goal is to select a winner who would beat the most other competitors in a round robin (i.e., maximize the Copeland score), and find them lacking. Our primary result establishes the approximation ratio of a randomly-seeded SE bracket is 2^{- Theta(sqrt{log n})}; this is underwhelming considering a 1/2 ratio is achieved by choosing a winner uniformly at random. We also establish that a generalized version of the SE bracket performs nearly as poorly, with an approximation ratio of 2^{- Omega(sqrt[4]{log n})}, addressing a decade-old open question in the voting tree literature.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11228Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11229
The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy and Li 2016] and [Chekuri and Ene 2013]. However, the problem is hard to approximate within polynomial factors on directed graphs, for any constant congestion [Chuzhoy, Kim and Li 2016].Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands. We extend their result by obtaining a polylogarithmic approximation with constant congestion on arbitrary directed minor-free graphs, for the case of symmetric demands.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11229Rainbow Coloring Hardness via Low Sensitivity Polymorphisms
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11230
A k-uniform hypergraph is said to be r-rainbow colorable if there is an r-coloring of its vertices such that every hyperedge intersects all r color classes. Given as input such a hypergraph, finding a r-rainbow coloring of it is NP-hard for all k >= 3 and r >= 2. Therefore, one settles for finding a rainbow coloring with fewer colors (which is an easier task). When r=k (the maximum possible value), i.e., the hypergraph is k-partite, one can efficiently 2-rainbow color the hypergraph, i.e., 2-color its vertices so that there are no monochromatic edges. In this work we consider the next smaller value of r=k-1, and prove that in this case it is NP-hard to rainbow color the hypergraph with q := ceil[(k-2)/2] colors. In particular, for k <=6, it is NP-hard to 2-color (k-1)-rainbow colorable k-uniform hypergraphs. Our proof follows the algebraic approach to promise constraint satisfaction problems. It proceeds by characterizing the polymorphisms associated with the approximate rainbow coloring problem, which are rainbow colorings of some product hypergraphs on vertex set [r]^n. We prove that any such polymorphism f: [r]^n -> [q] must be C-fixing, i.e., there is a small subset S of C coordinates and a setting a in [q]^S such that fixing x_{|S} = a determines the value of f(x). The key step in our proof is bounding the sensitivity of certain rainbow colorings, thereby arguing that they must be juntas. Armed with the C-fixing characterization, our NP-hardness is obtained via a reduction from smooth Label Cover.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11230Syntactic Separation of Subset Satisfiability Problems
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11231
Variants of the Exponential Time Hypothesis (ETH) have been used to derive lower bounds on the time complexity for certain problems, so that the hardness results match long-standing algorithmic results. In this paper, we consider a syntactically defined class of problems, and give conditions for when problems in this class require strongly exponential time to approximate to within a factor of (1-epsilon) for some constant epsilon > 0, assuming the Gap Exponential Time Hypothesis (Gap-ETH), versus when they admit a PTAS. Our class includes a rich set of problems from additive combinatorics, computational geometry, and graph theory. Our hardness results also match the best known algorithmic results for these problems.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11231Malleable Scheduling Beyond Identical Machines
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11232
In malleable job scheduling, jobs can be executed simultaneously on multiple machines with the processing time depending on the number of allocated machines. Jobs are required to be executed non-preemptively and in unison, in the sense that they occupy, during their execution, the same time interval over all the machines of the allocated set. In this work, we study generalizations of malleable job scheduling inspired by standard scheduling on unrelated machines. Specifically, we introduce a general model of malleable job scheduling, where each machine has a (possibly different) speed for each job, and the processing time of a job j on a set of allocated machines S depends on the total speed of S for j. For machines with unrelated speeds, we show that the optimal makespan cannot be approximated within a factor less than e/(e-1), unless P = NP. On the positive side, we present polynomial-time algorithms with approximation ratios 2e/(e-1) for machines with unrelated speeds, 3 for machines with uniform speeds, and 7/3 for restricted assignments on identical machines. Our algorithms are based on deterministic LP rounding and result in sparse schedules, in the sense that each machine shares at most one job with other machines. We also prove lower bounds on the integrality gap of 1+phi for unrelated speeds (phi is the golden ratio) and 2 for uniform speeds and restricted assignments. To indicate the generality of our approach, we show that it also yields constant factor approximation algorithms (i) for minimizing the sum of weighted completion times; and (ii) a variant where we determine the effective speed of a set of allocated machines based on the L_p norm of their speeds.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11232On the Cost of Essentially Fair Clusterings
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11233
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11233The Maximum Exposure Problem
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11234
Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11234Small Space Stream Summary for Matroid Center
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11235
In the matroid center problem, which generalizes the k-center problem, we need to pick a set of centers that is an independent set of a matroid with rank r. We study this problem in streaming, where elements of the ground set arrive in the stream. We first show that any randomized one-pass streaming algorithm that computes a better than Delta-approximation for partition-matroid center must use Omega(r^2) bits of space, where Delta is the aspect ratio of the metric and can be arbitrarily large. This shows a quadratic separation between matroid center and k-center, for which the Doubling algorithm [Charikar et al., 1997] gives an 8-approximation using O(k)-space and one pass. To complement this, we give a one-pass algorithm for matroid center that stores at most O(r^2 log(1/epsilon)/epsilon) points (viz., stream summary) among which a (7+epsilon)-approximate solution exists, which can be found by brute force, or a (17+epsilon)-approximation can be found with an efficient algorithm. If we are allowed a second pass, we can compute a (3+epsilon)-approximation efficiently.We also consider the problem of matroid center with z outliers and give a one-pass algorithm that outputs a set of O((r^2+rz)log(1/epsilon)/epsilon) points that contains a (15+epsilon)-approximate solution. Our techniques extend to knapsack center and knapsack center with z outliers in a straightforward way, and we get algorithms that use space linear in the size of a largest feasible set (as opposed to quadratic space for matroid center).Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11235Improved Bounds for Open Online Dial-a-Ride on the Line
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11236
We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates online Dial-a-Ride on the line from online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11236Improved Online Algorithms for Knapsack and GAP in the Random Order Model
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11237
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival. We study the online variant in the random order model where the input sequence is a uniform random permutation of the item set.We develop a randomized (1/6.65)-competitive algorithm for this problem, outperforming the current best algorithm of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)]. Our algorithm is based on two new insights: We introduce a novel algorithmic approach that employs two given algorithms, optimized for restricted item classes, sequentially on the input sequence. In addition, we study and exploit the relationship of the knapsack problem to the 2-secretary problem.The generalized assignment problem (GAP) includes, besides the knapsack problem, several important problems related to scheduling and matching. We show that in the same online setting, applying the proposed sequential approach yields a (1/6.99)-competitive randomized algorithm for GAP. Again, our proposed algorithm outperforms the current best result of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)].Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11237Fast and Deterministic Approximations for k-Cut
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11238
In an undirected graph, a k-cut is a set of edges whose removal breaks the graph into at least k connected components. The minimum weight k-cut can be computed in n^O(k) time, but when k is treated as part of the input, computing the minimum weight k-cut is NP-Hard [Goldschmidt and Hochbaum, 1994]. For poly(m,n,k)-time algorithms, the best possible approximation factor is essentially 2 under the small set expansion hypothesis [Manurangsi, 2017]. Saran and Vazirani [1995] showed that a (2 - 2/k)-approximately minimum weight k-cut can be computed via O(k) minimum cuts, which implies a O~(km) randomized running time via the nearly linear time randomized min-cut algorithm of Karger [2000]. Nagamochi and Kamidoi [2007] showed that a (2 - 2/k)-approximately minimum weight k-cut can be computed deterministically in O(mn + n^2 log n) time. These results prompt two basic questions. The first concerns the role of randomization. Is there a deterministic algorithm for 2-approximate k-cuts matching the randomized running time of O~(km)? The second question qualitatively compares minimum cut to 2-approximate minimum k-cut. Can 2-approximate k-cuts be computed as fast as the minimum cut - in O~(m) randomized time?We give a deterministic approximation algorithm that computes (2 + eps)-minimum k-cuts in O(m log^3 n / eps^2) time, via a (1 + eps)-approximation for an LP relaxation of k-cut.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11238Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11239
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal. In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within ~~0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within ~~0.929. In both cases, the previous best hardness results were the same as the hardness of the corresponding unconstrained Max-2-CSP (~~0.878 for Max-Cut, and ~~0.940 for Max-2-Sat).The hardness for Max-2-Sat applies to monotone Max-2-Sat instances, meaning that we also obtain tight inapproximability for the Max-k-Vertex-Cover problem.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11239Robust Appointment Scheduling with Heterogeneous Costs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11240
Designing simple appointment systems that under uncertainty in service times, try to achieve both high utilization of expensive medical equipment and personnel as well as short waiting time for patients, has long been an interesting and challenging problem in health care. We consider a robust version of the appointment scheduling problem, introduced by Mittal et al. (2014), with the goal of finding simple and easy-to-use algorithms. Previous work focused on the special case where per-unit costs due to under-utilization of equipment/personnel are homogeneous i.e., costs are linear and identical. We consider the heterogeneous case and devise an LP that has a simple closed-form solution. This solution yields the first constant-factor approximation for the problem. We also find special cases beyond homogeneous costs where the LP leads to closed form optimal schedules. Our approach and results extend more generally to convex piece-wise linear costs.For the case where the order of patients is changeable, we focus on linear costs and show that the problem is strongly NP-hard when the under-utilization costs are heterogeneous. For changeable order with homogeneous under-utilization costs, it was previously shown that an EPTAS exists. We instead find an extremely simple, ratio-based ordering that is 1.0604 approximate.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11240Collapsing Superstring Conjecture
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11241
In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits 2 11/23-approximation in polynomial time (Mucha, SODA'13). While this algorithm and its analysis are technically involved, the 30 years old Greedy Conjecture claims that the trivial and efficient Greedy Algorithm gives a 2-approximation for SCS. We develop a graph-theoretic framework for studying approximation algorithms for SCS. The framework is reminiscent of the classical 2-approximation for Traveling Salesman: take two copies of an optimal solution, apply a trivial edge-collapsing procedure, and get an approximate solution. In this framework, we observe two surprising properties of SCS solutions, and we conjecture that they hold for all input instances. The first conjecture, that we call Collapsing Superstring conjecture, claims that there is an elementary way to transform any solution repeated twice into the same graph G. This conjecture would give an elementary 2-approximate algorithm for SCS. The second conjecture claims that not only the resulting graph G is the same for all solutions, but that G can be computed by an elementary greedy procedure called Greedy Hierarchical Algorithm.While the second conjecture clearly implies the first one, perhaps surprisingly we prove their equivalence. We support these equivalent conjectures by giving a proof for the special case where all input strings have length at most 3 (which until recently had been the only case where the Greedy Conjecture was proven). We also tested our conjectures on millions of instances of SCS.We prove that the standard Greedy Conjecture implies Greedy Hierarchical Conjecture, while the latter is sufficient for an efficient greedy 2-approximate approximation of SCS. Except for its (conjectured) good approximation ratio, the Greedy Hierarchical Algorithm provably finds a 3.5-approximation, and finds exact solutions for the special cases where we know polynomial time (not greedy) exact algorithms: (1) when the input strings form a spectrum of a string (2) when all input strings have length at most 2.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11241Improved Algorithms for Time Decay Streams
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11242
In the time-decay model for data streams, elements of an underlying data set arrive sequentially with the recently arrived elements being more important. A common approach for handling large data sets is to maintain a coreset, a succinct summary of the processed data that allows approximate recovery of a predetermined query. We provide a general framework that takes any offline-coreset and gives a time-decay coreset for polynomial time decay functions.We also consider the exponential time decay model for k-median clustering, where we provide a constant factor approximation algorithm that utilizes the online facility location algorithm. Our algorithm stores O(k log(h Delta)+h) points where h is the half-life of the decay function and Delta is the aspect ratio of the dataset. Our techniques extend to k-means clustering and M-estimators as well.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11242Approximation Algorithms for Partially Colorable Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11243
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For alpha <= 1 and k in Z^+, we say that a graph G=(V,E) is alpha-partially k-colorable, if there exists a subset S subset V of cardinality |S| >= alpha |V| such that the graph induced on S is k-colorable. Partial k-colorability is a more robust structural property of a graph than k-colorability. For graphs that arise in practice, partial k-colorability might be a better notion to use than k-colorability, since data arising in practice often contains various forms of noise.We give a polynomial time algorithm that takes as input a (1 - epsilon)-partially 3-colorable graph G and a constant gamma in [epsilon, 1/10], and colors a (1 - epsilon/gamma) fraction of the vertices using O~(n^{0.25 + O(gamma^{1/2})}) colors. We also study natural semi-random families of instances of partially 3-colorable graphs and partially 2-colorable graphs, and give stronger bi-criteria approximation guarantees for these family of instances.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11243Towards Optimal Moment Estimation in Streaming and Distributed Models
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11244
One of the oldest problems in the data stream model is to approximate the p-th moment ||X||_p^p = sum_{i=1}^n X_i^p of an underlying non-negative vector X in R^n, which is presented as a sequence of poly(n) updates to its coordinates. Of particular interest is when p in (0,2]. Although a tight space bound of Theta(epsilon^-2 log n) bits is known for this problem when both positive and negative updates are allowed, surprisingly there is still a gap in the space complexity of this problem when all updates are positive. Specifically, the upper bound is O(epsilon^-2 log n) bits, while the lower bound is only Omega(epsilon^-2 + log n) bits. Recently, an upper bound of O~(epsilon^-2 + log n) bits was obtained under the assumption that the updates arrive in a random order.We show that for p in (0, 1], the random order assumption is not needed. Namely, we give an upper bound for worst-case streams of O~(epsilon^-2 + log n) bits for estimating |X |_p^p. Our techniques also give new upper bounds for estimating the empirical entropy in a stream. On the other hand, we show that for p in (1,2], in the natural coordinator and blackboard distributed communication topologies, there is an O~(epsilon^-2) bit max-communication upper bound based on a randomized rounding scheme. Our protocols also give rise to protocols for heavy hitters and approximate matrix product. We generalize our results to arbitrary communication topologies G, obtaining an O~(epsilon^2 log d) max-communication upper bound, where d is the diameter of G. Interestingly, our upper bound rules out natural communication complexity-based approaches for proving an Omega(epsilon^-2 log n) bit lower bound for p in (1,2] for streaming algorithms. In particular, any such lower bound must come from a topology with large diameter.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11244The Complexity of Partial Function Extension for Coverage Functions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11245
Coverage functions are an important subclass of submodular functions, finding applications in machine learning, game theory, social networks, and facility location. We study the complexity of partial function extension to coverage functions. That is, given a partial function consisting of a family of subsets of [m] and a value at each point, does there exist a coverage function defined on all subsets of [m] that extends this partial function? Partial function extension is previously studied for other function classes, including boolean functions and convex functions, and is useful in many fields, such as obtaining bounds on learning these function classes.We show that determining extendibility of a partial function to a coverage function is NP-complete, establishing in the process that there is a polynomial-sized certificate of extendibility. The hardness also gives us a lower bound for learning coverage functions. We then study two natural notions of approximate extension, to account for errors in the data set. The two notions correspond roughly to multiplicative point-wise approximation and additive L_1 approximation. We show upper and lower bounds for both notions of approximation. In the second case we obtain nearly tight bounds.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11245Almost Optimal Classical Approximation Algorithms for a Quantum Generalization of Max-Cut
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11246
Approximation algorithms for constraint satisfaction problems (CSPs) are a central direction of study in theoretical computer science. In this work, we study classical product state approximation algorithms for a physically motivated quantum generalization of Max-Cut, known as the quantum Heisenberg model. This model is notoriously difficult to solve exactly, even on bipartite graphs, in stark contrast to the classical setting of Max-Cut. Here we show, for any interaction graph, how to classically and efficiently obtain approximation ratios 0.649 (anti-feromagnetic XY model) and 0.498 (anti-ferromagnetic Heisenberg XYZ model). These are almost optimal; we show that the best possible ratios achievable by a product state for these models is 2/3 and 1/2, respectively.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11246Maximizing Covered Area in the Euclidean Plane with Connectivity Constraint
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11247
Given a set D of n unit disks in the plane and an integer k <= n, the maximum area connected subset problem asks for a set D' subseteq D of size k that maximizes the area of the union of disks, under the constraint that this union is connected. This problem is motivated by wireless router deployment and is a special case of maximizing a submodular function under a connectivity constraint. We prove that the problem is NP-hard and analyze a greedy algorithm, proving that it is a 1/2-approximation. We then give a polynomial-time approximation scheme (PTAS) for this problem with resource augmentation, i.e., allowing an additional set of epsilon k disks that are not drawn from the input. Additionally, for two special cases of the problem we design a PTAS without resource augmentation.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11247Robust Correlation Clustering
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11248
In this paper, we introduce and study the Robust-Correlation-Clustering problem: given a graph G = (V,E) where every edge is either labeled + or - (denoting similar or dissimilar pairs of vertices), and a parameter m, the goal is to delete a set D of m vertices, and partition the remaining vertices V \ D into clusters to minimize the cost of the clustering, which is the sum of the number of + edges with end-points in different clusters and the number of - edges with end-points in the same cluster. This generalizes the classical Correlation-Clustering problem which is the special case when m = 0. Correlation clustering is useful when we have (only) qualitative information about the similarity or dissimilarity of pairs of points, and Robust-Correlation-Clustering equips this model with the capability to handle noise in datasets.In this work, we present a constant-factor bi-criteria algorithm for Robust-Correlation-Clustering on complete graphs (where our solution is O(1)-approximate w.r.t the cost while however discarding O(1) m points as outliers), and also complement this by showing that no finite approximation is possible if we do not violate the outlier budget. Our algorithm is very simple in that it first does a simple LP-based pre-processing to delete O(m) vertices, and subsequently runs a particular Correlation-Clustering algorithm ACNAlg [Ailon et al., 2005] on the residual instance. We then consider general graphs, and show (O(log n), O(log^2 n)) bi-criteria algorithms while also showing a hardness of alpha_MC on both the cost and the outlier violation, where alpha_MC is the lower bound for the Minimum-Multicut problem.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11248Counting Independent Sets and Colorings on Random Regular Bipartite Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11249
We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11249The Expected Number of Maximal Points of the Convolution of Two 2-D Distributions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11250
The Maximal points in a set S are those that are not dominated by any other point in S. Such points arise in multiple application settings and are called by a variety of different names, e.g., maxima, Pareto optimums, skylines. Their ubiquity has inspired a large literature on the expected number of maxima in a set S of n points chosen IID from some distribution. Most such results assume that the underlying distribution is uniform over some spatial region and strongly use this uniformity in their analysis.This research was initially motivated by the question of how this expected number changes if the input distribution is perturbed by random noise. More specifically, let B_p denote the uniform distribution from the 2-dimensional unit ball in the metric L_p. Let delta B_q denote the 2-dimensional L_q-ball, of radius delta and B_p + delta B_q be the convolution of the two distributions, i.e., a point v in B_p is reported with an error chosen from delta B_q. The question is how the expected number of maxima change as a function of delta. Although the original motivation is for small delta, the problem is well defined for any delta and our analysis treats the general case. More specifically, we study, as a function of n,delta, the expected number of maximal points when the n points in S are chosen IID from distributions of the type B_p + delta B_q where p,q in {1,2,infty} for delta > 0 and also of the type B_infty + delta B_q where q in [1,infty) for delta > 0.For fixed p,q we show that this function changes "smoothly" as a function of delta but that this smooth behavior sometimes transitions unexpectedly between different growth behaviors.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11250On a Connectivity Threshold for Colorings of Random Graphs and Hypergraphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11251
Let Omega_q=Omega_q(H) denote the set of proper [q]-colorings of the hypergraph H. Let Gamma_q be the graph with vertex set Omega_q where two vertices are adjacent iff the corresponding colorings differ in exactly one vertex. We show that if H=H_{n,m;k}, k >= 2, the random k-uniform hypergraph with V=[n] and m=dn/k hyperedges then w.h.p. Gamma_q is connected if d is sufficiently large and q >~ (d/log d)^{1/(k-1)}. This is optimal to the first order in d. Furthermore, with a few more colors, we find that the diameter of Gamma_q is O(n) w.h.p, where the hidden constant depends on d. So, with this choice of d,q, the natural Glauber Dynamics Markov Chain on Omega_q is ergodic w.h.p.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11251Slow Mixing of Glauber Dynamics for the Six-Vertex Model in the Ordered Phases
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11252
The six-vertex model in statistical physics is a weighted generalization of the ice model on Z^2 (i.e., Eulerian orientations) and the zero-temperature three-state Potts model (i.e., proper three-colorings). The phase diagram of the model represents its physical properties and suggests where local Markov chains will be efficient. In this paper, we analyze the mixing time of Glauber dynamics for the six-vertex model in the ordered phases. Specifically, we show that for all Boltzmann weights in the ferroelectric phase, there exist boundary conditions such that local Markov chains require exponential time to converge to equilibrium. This is the first rigorous result bounding the mixing time of Glauber dynamics in the ferroelectric phase. Our analysis demonstrates a fundamental connection between correlated random walks and the dynamics of intersecting lattice path models (or routings). We analyze the Glauber dynamics for the six-vertex model with free boundary conditions in the antiferroelectric phase and significantly extend the region for which local Markov chains are known to be slow mixing. This result relies on a Peierls argument and novel properties of weighted non-backtracking walks.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11252Lifted Multiplicity Codes and the Disjoint Repair Group Property
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11253
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization of their construction, which we call lifted multiplicity codes. These are multivariate polynomial codes whose restriction to any line is a codeword of a multiplicity code (Kopparty, Saraf, Yekhanin 2014). We show that lifted multiplicity codes have a better trade-off between redundancy and a notion of locality called the t-disjoint-repair-group property than previously known constructions. More precisely, we show that, for t <=sqrt{N}, lifted multiplicity codes with length N and redundancy O(t^{0.585} sqrt{N}) have the property that any symbol of a codeword can be reconstructed in t different ways, each using a disjoint subset of the other coordinates. This gives the best known trade-off for this problem for any super-constant t < sqrt{N}. We also give an alternative analysis of lifted Reed Solomon codes using dual codes, which may be of independent interest.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11253Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11254
We study the r-complex contagion influence maximization problem. In the influence maximization problem, one chooses a fixed number of initial seeds in a social network to maximize the spread of their influence. In the r-complex contagion model, each uninfected vertex in the network becomes infected if it has at least r infected neighbors.In this paper, we focus on a random graph model named the stochastic hierarchical blockmodel, which is a special case of the well-studied stochastic blockmodel. When the graph is not exceptionally sparse, in particular, when each edge appears with probability omega (n^{-(1+1/r)}), under certain mild assumptions, we prove that the optimal seeding strategy is to put all the seeds in a single community. This matches the intuition that in a nonsubmodular cascade model placing seeds near each other creates synergy. However, it sharply contrasts with the intuition for submodular cascade models (e.g., the independent cascade model and the linear threshold model) in which nearby seeds tend to erode each others' effects.Finally, we show that this observation yields a polynomial time dynamic programming algorithm which outputs optimal seeds if each edge appears with a probability either in omega (n^{-(1+1/r)}) or in o (n^{-2}).Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11254Direct Sum Testing: The General Case
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11255
A function f:[n_1] x ... x[n_d]->F_2 is a direct sum if it is of the form f (a_1,...,a_d) = f_1(a_1) oplus ... oplus f_d (a_d), for some d functions f_i:[n_i]->F_2 for all i=1,..., d, and where n_1,...,n_d in N. We present a 4-query test which distinguishes between direct sums and functions that are far from them. The test relies on the BLR linearity test (Blum, Luby, Rubinfeld, 1993) and on the direct product test constructed by Dinur & Steurer (2014).We also present a different test, which queries the function (d+1) times, but is easier to analyze.In multiplicative +/- 1 notation, this reads as follows. A d-dimensional tensor with +/- 1 entries is called a tensor product if it is a tensor product of d vectors with +/- 1 entries, or equivalently, if it is of rank 1. The presented tests can be read as tests for distinguishing between tensor products and tensors that are far from being tensor products.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11255Fast Algorithms at Low Temperatures via Markov Chains
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11256
For spin systems, such as the hard-core model on independent sets weighted by fugacity lambda>0, efficient algorithms for the associated approximate counting/sampling problems typically apply in the high-temperature region, corresponding to low fugacity. Recent work of Jenssen, Keevash and Perkins (2019) yields an FPTAS for approximating the partition function (and an efficient sampling algorithm) on bounded-degree (bipartite) expander graphs for the hard-core model at sufficiently high fugacity, and also the ferromagnetic Potts model at sufficiently low temperatures. Their method is based on using the cluster expansion to obtain a complex zero-free region for the partition function of a polymer model, and then approximating this partition function using the polynomial interpolation method of Barvinok. We present a simple discrete-time Markov chain for abstract polymer models, and present an elementary proof of rapid mixing of this new chain under sufficient decay of the polymer weights. Applying these general polymer results to the hard-core and ferromagnetic Potts models on bounded-degree (bipartite) expander graphs yields fast algorithms with running time O(n log n) for the Potts model and O(n^2 log n) for the hard-core model, in contrast to typical running times of n^{O(log Delta)} for algorithms based on Barvinok's polynomial interpolation method on graphs of maximum degree Delta. In addition, our approach via our polymer model Markov chain is conceptually simpler as it circumvents the zero-free analysis and the generalization to complex parameters. Finally, we combine our results for the hard-core and ferromagnetic Potts models with standard Markov chain comparison tools to obtain polynomial mixing time for the usual spin system Glauber dynamics restricted to even and odd or "red" dominant portions of the respective state spaces.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11256Deterministic Approximation of Random Walks in Small Space
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11257
We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph G, a positive integer r, and a set S of vertices, approximates the conductance of S in the r-step random walk on G to within a factor of 1+epsilon, where epsilon>0 is an arbitrarily small constant. More generally, our algorithm computes an epsilon-spectral approximation to the normalized Laplacian of the r-step walk.Our algorithm combines the derandomized square graph operation [Eyal Rozenman and Salil Vadhan, 2005], which we recently used for solving Laplacian systems in nearly logarithmic space [Murtagh et al., 2017], with ideas from [Cheng et al., 2015], which gave an algorithm that is time-efficient (while ours is space-efficient) and randomized (while ours is deterministic) for the case of even r (while ours works for all r). Along the way, we provide some new results that generalize technical machinery and yield improvements over previous work. First, we obtain a nearly linear-time randomized algorithm for computing a spectral approximation to the normalized Laplacian for odd r. Second, we define and analyze a generalization of the derandomized square for irregular graphs and for sparsifying the product of two distinct graphs. As part of this generalization, we also give a strongly explicit construction of expander graphs of every size.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11257Two-Source Condensers with Low Error and Small Entropy Gap via Entropy-Resilient Functions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11258
In their seminal work, Chattopadhyay and Zuckerman (STOC'16) constructed a two-source extractor with error epsilon for n-bit sources having min-entropy {polylog}(n/epsilon). Unfortunately, the construction's running-time is {poly}(n/epsilon), which means that with polynomial-time constructions, only polynomially-small errors are possible. Our main result is a {poly}(n,log(1/epsilon))-time computable two-source condenser. For any k >= {polylog}(n/epsilon), our condenser transforms two independent (n,k)-sources to a distribution over m = k-O(log(1/epsilon)) bits that is epsilon-close to having min-entropy m - o(log(1/epsilon)). Hence, achieving entropy gap of o(log(1/epsilon)).The bottleneck for obtaining low error in recent constructions of two-source extractors lies in the use of resilient functions. Informally, this is a function that receives input bits from r players with the property that the function's output has small bias even if a bounded number of corrupted players feed adversarial inputs after seeing the inputs of the other players. The drawback of using resilient functions is that the error cannot be smaller than ln r/r. This, in return, forces the running time of the construction to be polynomial in 1/epsilon.A key component in our construction is a variant of resilient functions which we call entropy-resilient functions. This variant can be seen as playing the above game for several rounds, each round outputting one bit. The goal of the corrupted players is to reduce, with as high probability as they can, the min-entropy accumulated throughout the rounds. We show that while the bias decreases only polynomially with the number of players in a one-round game, their success probability decreases exponentially in the entropy gap they are attempting to incur in a repeated game.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11258Efficient Average-Case Population Recovery in the Presence of Insertions and Deletions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11259
A number of recent works have considered the trace reconstruction problem, in which an unknown source string x in {0,1}^n is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a trace of x. The goal is to reconstruct the original string x from independent traces of x. While the asymptotically best algorithms known for worst-case strings use exp(O(n^{1/3})) traces [De et al., 2017; Fedor Nazarov and Yuval Peres, 2017], several highly efficient algorithms are known [Yuval Peres and Alex Zhai, 2017; Nina Holden et al., 2018] for the average-case version of the problem, in which the source string x is chosen uniformly at random from {0,1}^n. In this paper we consider a generalization of the above-described average-case trace reconstruction problem, which we call average-case population recovery in the presence of insertions and deletions. In this problem, rather than a single unknown source string there is an unknown distribution over s unknown source strings x^1,...,x^s in {0,1}^n, and each sample given to the algorithm is independently generated by drawing some x^i from this distribution and returning an independent trace of x^i. Building on the results of [Yuval Peres and Alex Zhai, 2017] and [Nina Holden et al., 2018], we give an efficient algorithm for the average-case population recovery problem in the presence of insertions and deletions. For any support size 1 <= s <= exp(Theta(n^{1/3})), for a 1-o(1) fraction of all s-element support sets {x^1,...,x^s} subset {0,1}^n, for every distribution D supported on {x^1,...,x^s}, our algorithm can efficiently recover D up to total variation distance at most epsilon with high probability, given access to independent traces of independent draws from D. The running time of our algorithm is poly(n,s,1/epsilon) and its sample complexity is poly (s,1/epsilon,exp(log^{1/3} n)). This polynomial dependence on the support size s is in sharp contrast with the worst-case version of the problem (when x^1,...,x^s may be any strings in {0,1}^n), in which the sample complexity of the most efficient known algorithm [Frank Ban et al., 2019] is doubly exponential in s.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11259Improved Pseudorandom Generators from Pseudorandom Multi-Switching Lemmas
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11260
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11260Unconstraining Graph-Constrained Group Testing
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11261
In network tomography, one goal is to identify a small set of failed links in a network using as little information as possible. One way of setting up this problem is called graph-constrained group testing. Graph-constrained group testing is a variant of the classical combinatorial group testing problem, where the tests that one is allowed are additionally constrained by a graph. In this case, the graph is given by the underlying network topology.The main contribution of this work is to show that for most graphs, the constraints imposed by the graph are no constraint at all. That is, the number of tests required to identify the failed links in graph-constrained group testing is near-optimal even for the corresponding group testing problem with no graph constraints. Our approach is based on a simple randomized construction of tests. To analyze our construction, we prove new results about the size of giant components in randomly sparsified graphs.Finally, we provide empirical results which suggest that our connected-subgraph tests perform better not just in theory but also in practice, and in particular perform better on a real-world network topology.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11261Near-Neighbor Preserving Dimension Reduction for Doubling Subsets of l_1
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11262
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the Euclidean (l_2) metric, but much less for the Manhattan (l_1) metric. Our primary motivation is the approximate nearest neighbor problem in l_1. We exploit its reduction to the decision-with-witness version, called approximate near neighbor, which incurs a roughly logarithmic overhead. In 2007, Indyk and Naor, in the context of approximate nearest neighbors, introduced the notion of nearest neighbor-preserving embeddings. These are randomized embeddings between two metric spaces with guaranteed bounded distortion only for the distances between a query point and a point set. Such embeddings are known to exist for both l_2 and l_1 metrics, as well as for doubling subsets of l_2. The case that remained open were doubling subsets of l_1. In this paper, we propose a dimension reduction by means of a near neighbor-preserving embedding for doubling subsets of l_1. Our approach is to represent the pointset with a carefully chosen covering set, then randomly project the latter. We study two types of covering sets: c-approximate r-nets and randomly shifted grids, and we discuss the tradeoff between them in terms of preprocessing time and target dimension. We employ Cauchy variables: certain concentration bounds derived should be of independent interest.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11262Improved Strong Spatial Mixing for Colorings on Trees
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11263
Strong spatial mixing (SSM) is a form of correlation decay that has played an essential role in the design of approximate counting algorithms for spin systems. A notable example is the algorithm of Weitz (2006) for the hard-core model on weighted independent sets. We study SSM for the q-colorings problem on the infinite (d+1)-regular tree. Weak spatial mixing (WSM) captures whether the influence of the leaves on the root vanishes as the height of the tree grows. Jonasson (2002) established WSM when q>d+1. In contrast, in SSM, we first fix a coloring on a subset of internal vertices, and we again ask if the influence of the leaves on the root is vanishing. It was known that SSM holds on the (d+1)-regular tree when q>alpha d where alpha ~~ 1.763... is a constant that has arisen in a variety of results concerning random colorings. Here we improve on this bound by showing SSM for q>1.59d. Our proof establishes an L^2 contraction for the BP operator. For the contraction we bound the norm of the BP Jacobian by exploiting combinatorial properties of the coloring of the tree.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11263(Near) Optimal Adaptivity Gaps for Stochastic Multi-Value Probing
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11264
Consider a kidney-exchange application where we want to find a max-matching in a random graph. To find whether an edge e exists, we need to perform an expensive test, in which case the edge e appears independently with a known probability p_e. Given a budget on the total cost of the tests, our goal is to find a testing strategy that maximizes the expected maximum matching size.The above application is an example of the stochastic probing problem. In general the optimal stochastic probing strategy is difficult to find because it is adaptive - decides on the next edge to probe based on the outcomes of the probed edges. An alternate approach is to show the adaptivity gap is small, i.e., the best non-adaptive strategy always has a value close to the best adaptive strategy. This allows us to focus on designing non-adaptive strategies that are much simpler. Previous works, however, have focused on Bernoulli random variables that can only capture whether an edge appears or not. In this work we introduce a multi-value stochastic probing problem, which can also model situations where the weight of an edge has a probability distribution over multiple values.Our main technical contribution is to obtain (near) optimal bounds for the (worst-case) adaptivity gaps for multi-value stochastic probing over prefix-closed constraints. For a monotone submodular function, we show the adaptivity gap is at most 2 and provide a matching lower bound. For a weighted rank function of a k-extendible system (a generalization of intersection of k matroids), we show the adaptivity gap is between O(k log k) and k. None of these results were known even in the Bernoulli case where both our upper and lower bounds also apply, thereby resolving an open question of Gupta et al. [Gupta et al., 2017].Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11264Testing Odd Direct Sums Using High Dimensional Expanders
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11265
In this work, using methods from high dimensional expansion, we show that the property of k-direct-sum is testable for odd values of k . Previous work of [Kaufman and Lubotzky, 2014] could inherently deal only with the case that k is even, using a reduction to linearity testing. Interestingly, our work is the first to combine the topological notion of high dimensional expansion (called co-systolic expansion) with the combinatorial/spectral notion of high dimensional expansion (called colorful expansion) to obtain the result.The classical k-direct-sum problem applies to the complete complex; Namely it considers a function defined over all k-subsets of some n sized universe. Our result here applies to any collection of k-subsets of an n-universe, assuming this collection of subsets forms a high dimensional expander.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11265A Lower Bound for Sampling Disjoint Sets
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11266
Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x subseteq[n] and Bob ends up with a set y subseteq[n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant beta<1, this requires Omega(n) communication even to get within statistical distance 1-beta^n of the target distribution. Previously, Ambainis, Schulman, Ta-Shma, Vazirani, and Wigderson (FOCS 1998) proved that Omega(sqrt{n}) communication is required to get within some constant statistical distance epsilon>0 of the uniform distribution over all pairs of disjoint sets of size sqrt{n}.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11266Approximating the Noise Sensitivity of a Monotone Boolean Function
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11267
The noise sensitivity of a Boolean function f: {0,1}^n - > {0,1} is one of its fundamental properties. For noise parameter delta, the noise sensitivity is denoted as NS_{delta}[f]. This quantity is defined as follows: First, pick x = (x_1,...,x_n) uniformly at random from {0,1}^n, then pick z by flipping each x_i independently with probability delta. NS_{delta}[f] is defined to equal Pr [f(x) != f(z)]. Much of the existing literature on noise sensitivity explores the following two directions: (1) Showing that functions with low noise-sensitivity are structured in certain ways. (2) Mathematically showing that certain classes of functions have low noise sensitivity. Combined, these two research directions show that certain classes of functions have low noise sensitivity and therefore have useful structure. The fundamental importance of noise sensitivity, together with this wealth of structural results, motivates the algorithmic question of approximating NS_{delta}[f] given an oracle access to the function f. We show that the standard sampling approach is essentially optimal for general Boolean functions. Therefore, we focus on estimating the noise sensitivity of monotone functions, which form an important subclass of Boolean functions, since many functions of interest are either monotone or can be simply transformed into a monotone function (for example the class of unate functions consists of all the functions that can be made monotone by reorienting some of their coordinates [O'Donnell, 2014]). Specifically, we study the algorithmic problem of approximating NS_{delta}[f] for monotone f, given the promise that NS_{delta}[f] >= 1/n^{C} for constant C, and for delta in the range 1/n <= delta <= 1/2. For such f and delta, we give a randomized algorithm performing O((min(1,sqrt{n} delta log^{1.5} n))/(NS_{delta}[f]) poly (1/epsilon)) queries and approximating NS_{delta}[f] to within a multiplicative factor of (1 +/- epsilon). Given the same constraints on f and delta, we also prove a lower bound of Omega((min(1,sqrt{n} delta))/(NS_{delta}[f] * n^{xi})) on the query complexity of any algorithm that approximates NS_{delta}[f] to within any constant factor, where xi can be any positive constant. Thus, our algorithm's query complexity is close to optimal in terms of its dependence on n.We introduce a novel descending-ascending view of noise sensitivity, and use it as a central tool for the analysis of our algorithm. To prove lower bounds on query complexity, we develop a technique that reduces computational questions about query complexity to combinatorial questions about the existence of "thin" functions with certain properties. The existence of such "thin" functions is proved using the probabilistic method. These techniques also yield new lower bounds on the query complexity of approximating other fundamental properties of Boolean functions: the total influence and the bias.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11267Connectivity of Random Annulus Graphs and the Geometric Block Model
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11268
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11268A Local Stochastic Algorithm for Separation in Heterogeneous Self-Organizing Particle Systems
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11269
We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC '16) that can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM '11), the high-temperature expansion of the Ising model, and careful probabilistic arguments.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11269The Large-Error Approximate Degree of AC^0
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11270
We prove two new results about the inability of low-degree polynomials to uniformly approximate constant-depth circuits, even to slightly-better-than-trivial error. First, we prove a tight Omega~(n^{1/2}) lower bound on the threshold degree of the SURJECTIVITY function on n variables. This matches the best known threshold degree bound for any AC^0 function, previously exhibited by a much more complicated circuit of larger depth (Sherstov, FOCS 2015). Our result also extends to a 2^{Omega~(n^{1/2})} lower bound on the sign-rank of an AC^0 function, improving on the previous best bound of 2^{Omega(n^{2/5})} (Bun and Thaler, ICALP 2016). Second, for any delta>0, we exhibit a function f : {-1,1}^n -> {-1,1} that is computed by a circuit of depth O(1/delta) and is hard to approximate by polynomials in the following sense: f cannot be uniformly approximated to error epsilon=1-2^{-Omega(n^{1-delta})}, even by polynomials of degree n^{1-delta}. Our recent prior work (Bun and Thaler, FOCS 2017) proved a similar lower bound, but which held only for error epsilon=1/3.Our result implies 2^{Omega(n^{1-delta})} lower bounds on the complexity of AC^0 under a variety of basic measures such as discrepancy, margin complexity, and threshold weight. This nearly matches the trivial upper bound of 2^{O(n)} that holds for every function. The previous best lower bound on AC^0 for these measures was 2^{Omega(n^{1/2})} (Sherstov, FOCS 2015). Additional applications in learning theory, communication complexity, and cryptography are described.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11270String Matching: Communication, Circuits, and Learning
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11271
String matching is the problem of deciding whether a given n-bit string contains a given k-bit pattern. We study the complexity of this problem in three settings. - Communication complexity. For small k, we provide near-optimal upper and lower bounds on the communication complexity of string matching. For large k, our bounds leave open an exponential gap; we exhibit some evidence for the existence of a better protocol. - Circuit complexity. We present several upper and lower bounds on the size of circuits with threshold and DeMorgan gates solving the string matching problem. Similarly to the above, our bounds are near-optimal for small k. - Learning. We consider the problem of learning a hidden pattern of length at most k relative to the classifier that assigns 1 to every string that contains the pattern. We prove optimal bounds on the VC dimension and sample complexity of this problem.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11271Efficient Black-Box Identity Testing for Free Group Algebras
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11272
Hrubes and Wigderson [Pavel Hrubes and Avi Wigderson, 2014] initiated the study of noncommutative arithmetic circuits with division computing a noncommutative rational function in the free skew field, and raised the question of rational identity testing. For noncommutative formulas with inverses the problem can be solved in deterministic polynomial time in the white-box model [Ankit Garg et al., 2016; Ivanyos et al., 2018]. It can be solved in randomized polynomial time in the black-box model [Harm Derksen and Visu Makam, 2017], where the running time is polynomial in the size of the formula. The complexity of identity testing of noncommutative rational functions, in general, remains open for noncommutative circuits with inverses. We solve the problem for a natural special case. We consider expressions in the free group algebra F(X,X^{-1}) where X={x_1, x_2, ..., x_n}. Our main results are the following. 1) Given a degree d expression f in F(X,X^{-1}) as a black-box, we obtain a randomized poly(n,d) algorithm to check whether f is an identically zero expression or not. The technical contribution is an Amitsur-Levitzki type theorem [A. S. Amitsur and J. Levitzki, 1950] for F(X, X^{-1}). This also yields a deterministic identity testing algorithm (and even an expression reconstruction algorithm) that is polynomial time in the sparsity of the input expression. 2) Given an expression f in F(X,X^{-1}) of degree D and sparsity s, as black-box, we can check whether f is identically zero or not in randomized poly(n,log s, log D) time. This yields a randomized polynomial-time algorithm when D and s are exponential in n.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11272The Maximum Label Propagation Algorithm on Sparse Random Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11273
In the Maximum Label Propagation Algorithm (Max-LPA), each vertex draws a distinct random label. In each subsequent round, each vertex updates its label to the label that is most frequent among its neighbours (including its own label), breaking ties towards the larger label. It is known that this algorithm can detect communities in random graphs with planted communities if the graphs are very dense, by converging to a different consensus for each community. In [Kothapalli et al., 2013] it was also conjectured that the same result still holds for sparse graphs if the degrees are at least C log n. We disprove this conjecture by showing that even for degrees n^epsilon, for some epsilon>0, the algorithm converges without reaching consensus. In fact, we show that the algorithm does not even reach almost consensus, but converges prematurely resulting in orders of magnitude more communities.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11273Samplers and Extractors for Unbounded Functions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11274
Blasiok (SODA'18) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions f from {0,1}^m to the real numbers such that f(U_m) has subgaussian tails, and asked for explicit constructions. In this work, we give the first explicit constructions of subgaussian samplers (and in fact averaging samplers for the broader class of subexponential functions) that match the best known constructions of averaging samplers for [0,1]-bounded functions in the regime of parameters where the approximation error epsilon and failure probability delta are subconstant. Our constructions are established via an extension of the standard notion of randomness extractor (Nisan and Zuckerman, JCSS'96) where the error is measured by an arbitrary divergence rather than total variation distance, and a generalization of Zuckerman's equivalence (Random Struct. Alg.'97) between extractors and samplers. We believe that the framework we develop, and specifically the notion of an extractor for the Kullback-Leibler (KL) divergence, are of independent interest. In particular, KL-extractors are stronger than both standard extractors and subgaussian samplers, but we show that they exist with essentially the same parameters (constructively and non-constructively) as standard extractors.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11274Successive Minimum Spanning Trees
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11275
In a complete graph K_n with edge weights drawn independently from a uniform distribution U(0,1) (or alternatively an exponential distribution Exp(1)), let T_1 be the MST (the spanning tree of minimum weight) and let T_k be the MST after deletion of the edges of all previous trees T_i, i<k. We show that each tree's weight w(T_k) converges in probability to a constant gamma_k with 2k-2 sqrt k < gamma_k < 2k+2 sqrt k, and we conjecture that gamma_k = 2k-1+o(1). The problem is distinct from that of [Alan Frieze and Tony Johansson, 2018], finding k MSTs of combined minimum weight, and the combined cost for two trees in their problem is, asymptotically, strictly smaller than our gamma_1+gamma_2.Our results also hold (and mostly are derived) in a multigraph model where edge weights for each vertex pair follow a Poisson process; here we additionally have E(w(T_k)) -> gamma_k. Thinking of an edge of weight w as arriving at time t=n w, Kruskal's algorithm defines forests F_k(t), each initially empty and eventually equal to T_k, with each arriving edge added to the first F_k(t) where it does not create a cycle. Using tools of inhomogeneous random graphs we obtain structural results including that C_1(F_k(t))/n, the fraction of vertices in the largest component of F_k(t), converges in probability to a function rho_k(t), uniformly for all t, and that a giant component appears in F_k(t) at a time t=sigma_k. We conjecture that the functions rho_k tend to time translations of a single function, rho_k(2k+x) -> rho_infty(x) as k -> infty, uniformly in x in R.Simulations and numerical computations give estimated values of gamma_k for small k, and support the conjectures stated above.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11275Simple Analysis of Sparse, Sign-Consistent JL
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11276
Allen-Zhu, Gelashvili, Micali, and Shavit construct a sparse, sign-consistent Johnson-Lindenstrauss distribution, and prove that this distribution yields an essentially optimal dimension for the correct choice of sparsity. However, their analysis of the upper bound on the dimension and sparsity requires a complicated combinatorial graph-based argument similar to Kane and Nelson's analysis of sparse JL. We present a simple, combinatorics-free analysis of sparse, sign-consistent JL that yields the same dimension and sparsity upper bounds as the original analysis. Our analysis also yields dimension/sparsity tradeoffs, which were not previously known. As with previous proofs in this area, our analysis is based on applying Markov's inequality to the pth moment of an error term that can be expressed as a quadratic form of Rademacher variables. Interestingly, we show that, unlike in previous work in the area, the traditionally used Hanson-Wright bound is not strong enough to yield our desired result. Indeed, although the Hanson-Wright bound is known to be optimal for gaussian degree-2 chaos, it was already shown to be suboptimal for Rademachers. Surprisingly, we are able to show a simple moment bound for quadratic forms of Rademachers that is sufficiently tight to achieve our desired result, which given the ubiquity of moment and tail bounds in theoretical computer science, is likely to be of broader interest.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11276Streaming Coreset Constructions for M-Estimators
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11277
We introduce a new method of maintaining a (k,epsilon)-coreset for clustering M-estimators over insertion-only streams. Let (P,w) be a weighted set (where w : P - > [0,infty) is the weight function) of points in a rho-metric space (meaning a set X equipped with a positive-semidefinite symmetric function D such that D(x,z) <=rho(D(x,y) + D(y,z)) for all x,y,z in X). For any set of points C, we define COST(P,w,C) = sum_{p in P} w(p) min_{c in C} D(p,c). A (k,epsilon)-coreset for (P,w) is a weighted set (Q,v) such that for every set C of k points, (1-epsilon)COST(P,w,C) <= COST(Q,v,C) <= (1+epsilon)COST(P,w,C). Essentially, the coreset (Q,v) can be used in place of (P,w) for all operations concerning the COST function. Coresets, as a method of data reduction, are used to solve fundamental problems in machine learning of streaming and distributed data.M-estimators are functions D(x,y) that can be written as psi(d(x,y)) where ({X}, d) is a true metric (i.e. 1-metric) space. Special cases of M-estimators include the well-known k-median (psi(x) =x) and k-means (psi(x) = x^2) functions. Our technique takes an existing offline construction for an M-estimator coreset and converts it into the streaming setting, where n data points arrive sequentially. To our knowledge, this is the first streaming construction for any M-estimator that does not rely on the merge-and-reduce tree. For example, our coreset for streaming metric k-means uses O(epsilon^{-2} k log k log n) points of storage. The previous state-of-the-art required storing at least O(epsilon^{-2} k log k log^{4} n) points.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11277Pairwise Independent Random Walks Can Be Slightly Unbounded
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11278
A family of problems that have been studied in the context of various streaming algorithms are generalizations of the fact that the expected maximum distance of a 4-wise independent random walk on a line over n steps is O(sqrt{n}). For small values of k, there exist k-wise independent random walks that can be stored in much less space than storing n random bits, so these properties are often useful for lowering space bounds. In this paper, we show that for all of these examples, 4-wise independence is required by demonstrating a pairwise independent random walk with steps uniform in +/- 1 and expected maximum distance Omega(sqrt{n} lg n) from the origin. We also show that this bound is tight for the first and second moment, i.e. the expected maximum square distance of a 2-wise independent random walk is always O(n lg^2 n). Also, for any even k >= 4, we show that the kth moment of the maximum distance of any k-wise independent random walk is O(n^{k/2}). The previous two results generalize to random walks tracking insertion-only streams, and provide higher moment bounds than currently known. We also prove a generalization of Kolmogorov's maximal inequality by showing an asymptotically equivalent statement that requires only 4-wise independent random variables with bounded second moments, which also generalizes a result of Blasiok.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11278Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11279
We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to e^{-f} where f:R^d -> R is mu-strongly convex and L-smooth (the condition number is kappa = L/mu). We show that the relaxation time (inverse of the spectral gap) of ideal HMC is O(kappa), improving on the previous best bound of O(kappa^{1.5}); we complement this with an example where the relaxation time is Omega(kappa). When implemented using a nearly optimal ODE solver, HMC returns an epsilon-approximate point in 2-Wasserstein distance using O~((kappa d)^{0.5} epsilon^{-1}) gradient evaluations per step and O~((kappa d)^{1.5}epsilon^{-1}) total time.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11279Exploring Differential Obliviousness
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11280
In a recent paper, Chan et al. [SODA '19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM '96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures.In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11280Thresholds in Random Motif Graphs
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11281
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11281Random-Cluster Dynamics in Z^2: Rapid Mixing with General Boundary Conditions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11282
The random-cluster (FK) model is a key tool for the study of phase transitions and for the design of efficient Markov chain Monte Carlo (MCMC) sampling algorithms for the Ising/Potts model. It is well-known that in the high-temperature region beta<beta_c(q) of the q-state Ising/Potts model on an n x n box Lambda_n of the integer lattice Z^2, spin correlations decay exponentially fast; this property holds even arbitrarily close to the boundary of Lambda_n and uniformly over all boundary conditions. A direct consequence of this property is that the corresponding single-site update Markov chain, known as the Glauber dynamics, mixes in optimal O(n^2 log{n}) steps on Lambda_{n} for all choices of boundary conditions. We study the effect of boundary conditions on the FK-dynamics, the analogous Glauber dynamics for the random-cluster model.On Lambda_n the random-cluster model with parameters (p,q) has a sharp phase transition at p = p_c(q). Unlike the Ising/Potts model, the random-cluster model has non-local interactions which can be forced by boundary conditions: external wirings of boundary vertices of Lambda_n. We consider the broad and natural class of boundary conditions that are realizable as a configuration on Z^2 \ Lambda_n. Such boundary conditions can have many macroscopic wirings and impose long-range correlations even at very high temperatures (p << p_c(q)). In this paper, we prove that when q>1 and p != p_c(q) the mixing time of the FK-dynamics is polynomial in n for every realizable boundary condition. Previously, for boundary conditions that do not carry long-range information (namely wired and free), Blanca and Sinclair (2017) had proved that the FK-dynamics in the same setting mixes in optimal O(n^2 log n) time. To illustrate the difficulties introduced by general boundary conditions, we also construct a class of non-realizable boundary conditions that induce slow (stretched-exponential) convergence at high temperatures.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11282On List Recovery of High-Rate Tensor Codes
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11283
We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) high-rate globally list recoverable code is approximately locally list recoverable, as well as globally list recoverable in probabilistic near-linear time. This was used in turn to give the first capacity-achieving list decodable codes with (1) local list decoding algorithms, and with (2) probabilistic near-linear time global list decoding algorithms. This also yielded constant-rate codes approaching the Gilbert-Varshamov bound with probabilistic near-linear time global unique decoding algorithms.In the current work we obtain the following results: 1) The tensor product of an efficient (poly-time) high-rate globally list recoverable code is globally list recoverable in deterministic near-linear time. This yields in turn the first capacity-achieving list decodable codes with deterministic near-linear time global list decoding algorithms. It also gives constant-rate codes approaching the Gilbert-Varshamov bound with deterministic near-linear time global unique decoding algorithms. 2) If the base code is additionally locally correctable, then the tensor product is (genuinely) locally list recoverable. This yields in turn (non-explicit) constant-rate codes approaching the Gilbert-Varshamov bound that are locally correctable with query complexity and running time N^{o(1)}. This improves over prior work by Gopi et. al. (SODA'17; IEEE Transactions on Information Theory'18) that only gave query complexity N^{epsilon} with rate that is exponentially small in 1/epsilon. 3) A nearly-tight combinatorial lower bound on output list size for list recovering high-rate tensor codes. This bound implies in turn a nearly-tight lower bound of N^{Omega(1/log log N)} on the product of query complexity and output list size for locally list recovering high-rate tensor codes.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11283Approximate F_2-Sketching of Valuation Functions
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11284
We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function f : F_2^n - > R with small expected squared error. We develop a general theory of linear sketching for such functions through which we analyze their dimension for most commonly studied types of valuation functions: additive, budget-additive, coverage, alpha-Lipschitz submodular and matroid rank functions. This gives a characterization of how many bits of information have to be stored about the input x so that one can compute f under additive updates to its coordinates.Our results are tight in most cases and we also give extensions to the distributional version of the problem where the input x in F_2^n is generated uniformly at random. Using known connections with dynamic streaming algorithms, both upper and lower bounds on dimension obtained in our work extend to the space complexity of algorithms evaluating f(x) under long sequences of additive updates to the input x presented as a stream. Similar results hold for simultaneous communication in a distributed setting.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11284Streaming Verification of Graph Computations via Graph Structure
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11285
We give new algorithms in the annotated data streaming setting - also known as verifiable data stream computation - for certain graph problems. This setting is meant to model outsourced computation, where a space-bounded verifier limited to sequential data access seeks to overcome its computational limitations by engaging a powerful prover, without needing to trust the prover. As is well established, several problems that admit no sublinear-space algorithms under traditional streaming do allow protocols using a sublinear amount of prover/verifier communication and sublinear-space verification. We give algorithms for many well-studied graph problems including triangle counting, its generalization to subgraph counting, maximum matching, problems about the existence (or not) of short paths, finding the shortest path between two vertices, and testing for an independent set. While some of these problems have been studied before, our results achieve new tradeoffs between space and communication costs that were hitherto unknown. In particular, two of our results disprove explicit conjectures of Thaler (ICALP, 2016) by giving triangle counting and maximum matching algorithms for n-vertex graphs, using o(n) space and o(n^2) communication.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11285Approximate Degree, Secret Sharing, and Concentration Phenomena
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11286
The epsilon-approximate degree deg~_epsilon(f) of a Boolean function f is the least degree of a real-valued polynomial that approximates f pointwise to within epsilon. A sound and complete certificate for approximate degree being at least k is a pair of probability distributions, also known as a dual polynomial, that are perfectly k-wise indistinguishable, but are distinguishable by f with advantage 1 - epsilon. Our contributions are:- We give a simple, explicit new construction of a dual polynomial for the AND function on n bits, certifying that its epsilon-approximate degree is Omega (sqrt{n log 1/epsilon}). This construction is the first to extend to the notion of weighted degree, and yields the first explicit certificate that the 1/3-approximate degree of any (possibly unbalanced) read-once DNF is Omega(sqrt{n}). It draws a novel connection between the approximate degree of AND and anti-concentration of the Binomial distribution.- We show that any pair of symmetric distributions on n-bit strings that are perfectly k-wise indistinguishable are also statistically K-wise indistinguishable with at most K^{3/2} * exp (-Omega (k^2/K)) error for all k < K <= n/64. This bound is essentially tight, and implies that any symmetric function f is a reconstruction function with constant advantage for a ramp secret sharing scheme that is secure against size-K coalitions with statistical error K^{3/2} * exp (-Omega (deg~_{1/3}(f)^2/K)) for all values of K up to n/64 simultaneously. Previous secret sharing schemes required that K be determined in advance, and only worked for f=AND. Our analysis draws another new connection between approximate degree and concentration phenomena. As a corollary of this result, we show that for any d <= n/64, any degree d polynomial approximating a symmetric function f to error 1/3 must have coefficients of l_1-norm at least K^{-3/2} * exp ({Omega (deg~_{1/3}(f)^2/d)}). We also show this bound is essentially tight for any d > deg~_{1/3}(f). These upper and lower bounds were also previously only known in the case f=AND.Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11286Improved Extractors for Recognizable and Algebraic Sources
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11287
Thu, 19 Sep 2019 00:00:00 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11287LIPIcs, Volume 144, ESA'19, Complete Volume
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11300
LIPIcs, Volume 144, ESA'19, Complete VolumeTue, 17 Sep 2019 15:02:09 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11300LIPIcs, Volume 143, WABI'19, Complete Volume
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11299
LIPIcs, Volume 143, WABI'19, Complete VolumeTue, 17 Sep 2019 15:01:56 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11299LIPIcs, Volume 142, COSIT'19, Complete Volume
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11298
LIPIcs, Volume 142, COSIT'19, Complete VolumeTue, 17 Sep 2019 15:01:37 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11298LIPIcs, Volume 141, ITP'19, Complete Volume
http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11297
LIPIcs, Volume 141, ITP'19, Complete VolumeTue, 17 Sep 2019 15:01:24 +0200http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=11297