19.03.17 - 24.03.17, Seminar 17121

Computational Complexity of Discrete Problems

Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

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 Unported license
Anna Gál, Michal Koucký, Oded Regev, and Till Tantau