New Deterministic Algorithms for Solving Parity Games

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

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 \(k^{O(\sqrt{k})}\cdot O(n^3)\) and general parity games in time \((p+k)^{O(\sqrt{k})} \cdot O(pnm)\), where p denotes the number of distinct priorities and m denotes the number of edges. For all games with \(k = o(n)\) this improves the previously fastest algorithm by Jurdziński, Paterson, and Zwick (SICOMP 2008).

We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Matthias Mnich
    • 1
  • Heiko Röglin
    • 1
  • Clemens Rösner
    • 1
  1. 1.Department of Computer ScienceUniversity of BonnBonnGermany

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