http://www.dagstuhl.de/17121

March 19 – 24 , 2017, Dagstuhl Seminar 17121

Computational Complexity of Discrete Problems

Organizers

Anna Gál (University of Texas – Austin, US)
Michal Koucký (Charles University – Prague, CZ)
Oded Regev (New York University, US)
Till Tantau (Universität zu Lübeck, DE)

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Dagstuhl Service Team

Documents

List of Participants
Shared Documents
Dagstuhl's Impact: Documents available
Dagstuhl Seminar Schedule [pdf]

Motivation

Computational complexity studies the amount of resources (such as time, space, randomness, or communication) that are necessary to solve computational problems in various models of computation. Finding efficient algorithms for solving computational tasks is crucial for practical applications and becomes even more important with the use of computers becoming part of everyday life. Despite a long line of research, for many problems that arise in practice it is not known if they can be solved efficiently – in particular in polynomial time.

Beside questions about the existence of polynomial time algorithms for problems like Satisfiability or Factoring where the best known algorithms run in exponential time, there is a huge class of practical problems where algorithms with polynomial running time (e.g. cubic or even quadratic time) are known, but it would be important to establish whether these running times are best possible, or to what extent they can be improved.

These fundamental questions motivate developments in various areas from algorithm design to circuit complexity, communication complexity and coding theory. During this Dagstuhl Seminar, we plan to discuss some of the most exciting recent developments in those areas related to computational complexity.

We briefly mention some of the developments here: An exciting new direction in the area of Boolean circuit complexity is the connection between circuits and the design of efficient algorithms. Known circuit constructions lead to faster algorithms and faster algorithms lead to circuit lower bounds. Information-theoretic techniques have led to major progress in our understanding of communication complexity, such as new methods to compress interactive communication, and new methods to prove lower bounds on communication complexity. In the last couple of years several exciting papers made progress towards resolving classical questions in communication complexity such as the log-rank conjecture and the "clique vs independent set" problem. In recent years, a new area of coding theory developed by considering error correcting codes with local decodability properties. Recent breakthrough results show the existence of various subexponential length locally decodable codes.

The seminar plans to bring together the leading experts working on research problems closely related to these topics. Besides the regular program including talks about recent research results, we plan to organize open problem sessions, and expect ongoing research discussions throughout the week in smaller groups. This seminar is a continuation of the series of Dagstuhl Seminars entitled "Computational Complexity of Discrete Problems" and formerly "Complexity of Boolean Functions."

License
  Creative Commons BY 3.0 DE
  Anna Gál and Michal Koucký and Oded Regev and Till Tantau

Dagstuhl Seminar Series

Classification

  • Data Structures / Algorithms / Complexity

Keywords

  • Computational complexity
  • Discrete problems
  • Turing machines
  • Circuits
  • Communication complexity
  • Lower bounds
  • Upper bounds
  • Coding theory
  • Pseudorandomness
  • Derandomization
  • Hardness of approximation

Book exhibition

Books from the participants of the current Seminar 

Book exhibition in the library, ground floor, during the seminar week.

Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.