https://www.dagstuhl.de/23111

March 12 – 17 , 2023, Dagstuhl Seminar 23111

Computational Complexity of Discrete Problems

Organizers

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

For support, please contact

Susanne Bach-Bernhard for administrative matters

Marsha Kleinbauer for scientific matters

Motivation

Computational complexity studies the amount of resources (such as time, space, randomness, or communication) necessary to solve computational problems in various models of computation – a crucial task both in theoretical and practical applications. Despite a long line of research, for many practical problems it is not known if they can be solved efficiently. Here, “efficiently” can refer to polynomial-time algorithms, whose existence is not known for problems like Satisfiability or Factoring , but also to cubic or even quadratic time, where it would be important to establish whether these running times are best possible for basic problems, to what extent they can be improved, and whether parallel algorithms allow improvements of the runtime.

These fundamental questions motivate developments in areas from algorithm design to circuit complexity, communication complexity and proof complexity. The seminar’s topics will include 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. Continuing a long and successful series, this Dagstuhl Seminar will build on previous experience and retain the series’ distinctive features, 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.

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.

Motivation text license
  Creative Commons BY 4.0
  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).

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.

Publications

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