Computational Complexity of Discrete Problems

Summary

Introduction and goals

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 discussed some of the most exciting recent developments in those areas related to computational complexity.

The seminar "Computational Complexity of Discrete Problems" has evolved out of the series of seminars entitled "Complexity of Boolean Functions," a topic that has been covered at Dagstuhl on a regular basis since the foundation of this research center. An important feature of the current research in computational complexity is the integration of ideas from different subareas of computational complexity and from other fields in computer science and mathematics. We have aimed to attract researchers from various subareas connected to core questions in boolean function complexity and foster further fruitful interactions.