research-article

Deciding parity games in quasipolynomial time

Authors:

Cristian S. Calude,

Bakhadyr Khoussainov,

Frank StephanAuthors Info & Claims

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

Pages 252 - 263

https://doi.org/10.1145/3055399.3055409

Published: 19 June 2017 Publication History

Abstract

It is shown that the parity game can be solved in quasipolynomial time. The parameterised parity game - with n nodes and m distinct values (aka colours or priorities) - is proven to be in the class of fixed parameter tractable (FPT) problems when parameterised over m. Both results improve known bounds, from runtime n^O(√n) to O(n^log(m)+6) and from an XP-algorithm with runtime O(n^Θ(m)) for fixed parameter m to an FPT-algorithm with runtime O(n⁵)+g(m), for some function g depending on m only. As an application it is proven that coloured Muller games with n nodes and m colours can be decided in time O((m^m · n)⁵); it is also shown that this bound cannot be improved to O((2^m · n)^c), for any c, unless FPT = W[1].

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Abstract 1 Introduction 2 The Complexity of the Parity Game 3 Parity Games versus Muller Games 4 Conclusion References

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Index Terms

Deciding parity games in quasipolynomial time
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Design and analysis of algorithms

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cover image ACM Conferences

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

June 2017

1268 pages

ISBN:9781450345286

DOI:10.1145/3055399

General Chairs:
Hamed Hatami
McGill University
,
Pierre McKenzie
Université de Montréal
,
Program Chair:
Valerie King
University of Victoria

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