https://www.dagstuhl.de/21121

March 21 – 26 , 2021, Dagstuhl Seminar 21121

Computational Complexity of Discrete Problems

Organizers

Anna Gál (University of Texas – Austin, US)
Meena Mahajan (Institute of Mathematical Sciences – Chennai, IN)
Rahul Santhanam (University of Oxford, GB)
Till Tantau (Universität zu Lübeck, DE)

For support, please contact

Jutka Gasiorowski for administrative matters

Michael Gerke for scientific matters

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 (such as 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 proof complexity. 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 subjects such as new lower bounds on formula size and circuit size, complexity measures of Boolean functions, the algorithmic method for proving lower bounds, fixed parameter tractability and hardness magnification, communication complexity and lifting techniques, as well as proof complexity.

The seminar is a continuation of the series of Dagstuhl Seminars entitled “Computational Complexity of Discrete Problems”. It will build on the long experience and retain the features that have made the series strong in the past, while also capitalizing on new and exciting developments in the area such as the proof of the Sensitivity Conjecture, new lower bounds and results on matrix rigidity via the algorithmic method, and the remarkable success of lifting techniques in translating lower bounds from query complexity to communication complexity and from proof complexity to circuit complexity.

Motivation text license
  Creative Commons BY 3.0 DE
  Anna Gál, Meena Mahajan, Rahul Santhanam, and Till Tantau

Dagstuhl Seminar Series

Classification

  • Computational Complexity
  • Data Structures And Algorithms

Keywords

  • Computational complexity
  • Circuit complexity
  • Communication complexity
  • Randomness
  • Lower bounds

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.