Computational Complexity of Discrete Problems

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. 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, to what extent they can be improved, and whether parallel algorithms allow improvements of the runtime.

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.

The bulk of the seminar will be taken up by talks and discussions. The topics will depend on and be driven by the participants, who will share their current research interests in talks, open problem sessions, and smaller group research. The list of topics will include – but not be limited to – subjects such as formula size – especially new results on lower bounds –, complexity measures of Boolean functions, lower bounds for algorithm runtimes arising from connections to Satisfiability problems, the relationship of circuit complexity and fixed parameter tractability, communication complexity, as well as deep learning and circuit complexity.

The seminar is a continuation of the series of Dagstuhl Seminars entitled “Computational Complexity of Discrete Problems” and formerly “Complexity of Boolean Functions.” It will build on the long experience and focus on what has made the series strong in the past: bringing together the leading experts and the exceptionally talented junior researchers to discuss the most exciting recent developments in different areas of computational complexity of discrete problems – both regarding recent results, but also regarding open problems.