New deterministic algorithms for solving parity games

Matthias Mnich, Heiko Roglin, Clemens Rosner

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n - k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite Parity games in time k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root k)) . O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdzinski, Paterson, and Zwick (SICOMP 2008).

We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. (C) 2018 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)73-95
Number of pages23
JournalDiscrete Optimization
Volume30
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Parity games
  • Fixed-parameter algorithms
  • Kernelization
  • Subexponential algorithms
  • SUBEXPONENTIAL ALGORITHM
  • INFINITE GAMES
  • WIDTH

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