New Deterministic Algorithms for Solving Parity Games

Matthias Mnich; Heiko Röglin; Clemens Rösner

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arXiv · 1512.03246

New Deterministic Algorithms for Solving Parity Games

Matthias Mnich·Heiko Röglin·Clemens Rösner

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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 $p$ 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 Jurdzi{ń}ski, 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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BibTeX RIS

Matthias Mnich, Heiko Röglin, Clemens Rösner. 2015-12-10. New Deterministic Algorithms for Solving Parity Games. https://arxiv.org/abs/1512.03246

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