### 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 n-kn-k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity games in time k o(k v ) ·o(n 3 ) ko(k)·o(n3)k^{o(\sqrt{k})}\cdot o(n^3) and general parity games in time (p+k) o(k v ) ·o(pnm) (p+k)o(k)·o(pnm)(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) k=o(n)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.

Original language | English |
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Title of host publication | LATIN 2016: Theoretical Informatics |

Publisher | Springer |

Pages | 634-645 |

ISBN (Electronic) | 978-3-662-49529-2 |

ISBN (Print) | 978-3-662-49528-5 |

DOIs | |

Publication status | Published - 2016 |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 9644 |

## Cite this

Mnich, M., Röglin, H., & Rösner, C. (2016). New deterministic algorithms for solving parity games. In

*LATIN 2016: Theoretical Informatics*(pp. 634-645). Springer. Lecture Notes in Computer Science, Vol.. 9644 https://doi.org/10.1007/978-3-662-49529-2_47