Abstract

The existence of polynomial-time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on the randomized subexponential simplex algorithms of Kalai and of Matoušek, Sharir, and Welzl. Randomness seems to play an essential role in these algorithms. We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games. The new algorithm, like the existing randomized subexponential algorithms, uses only polynomial space, and it is almost as fast as the randomized subexponential algorithms mentioned above.

MSC codes

  1. 68Q25
  2. 68Q60
  3. 91A05
  4. 91A43
  5. 91A50

Keywords

  1. analysis of algorithms and problem complexity
  2. specification and verification
  3. 2-player games
  4. games on graphs
  5. discrete-time games

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1519 - 1532
ISSN (online): 1095-7111

History

Submitted: 28 March 2007
Accepted: 18 July 2008
Published online: 12 November 2008

MSC codes

  1. 68Q25
  2. 68Q60
  3. 91A05
  4. 91A43
  5. 91A50

Keywords

  1. analysis of algorithms and problem complexity
  2. specification and verification
  3. 2-player games
  4. games on graphs
  5. discrete-time games

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