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Parity Games: Zielonka’s Algorithm in Quasi-Polynomial Time

Author Paweł Parys

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Paweł Parys
  • Institute of Informatics, University of Warsaw, Poland

Funding

Work supported by the National Science Centre, Poland (grant no. 2016/22/E/ST6/00041).

Acknowledgements

The author would like to thank Wojciech Czerwiński, Laure Daviaud, Marcin Jurdziński, Eryk Kopczyński, Ranko Lazić, Karoliina Lehtinen, and Igor Walukiewicz for all the discussions that preceded writing of this paper, and the anonymous reviewers of all versions of this paper for their valuable comments.

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Paweł Parys. Parity Games: Zielonka’s Algorithm in Quasi-Polynomial Time. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.MFCS.2019.10

Abstract

Calude, Jain, Khoussainov, Li, and Stephan (2017) proposed a quasi-polynomial-time algorithm solving parity games. After this breakthrough result, a few other quasi-polynomial-time algorithms were introduced; none of them is easy to understand. Moreover, it turns out that in practice they operate very slowly. On the other side there is Zielonka’s recursive algorithm, which is very simple, exponential in the worst case, and the fastest in practice. We combine these two approaches: we propose a small modification of Zielonka’s algorithm, which ensures that the running time is at most quasi-polynomial. In effect, we obtain a simple algorithm that solves parity games in quasi-polynomial time. We also hope that our algorithm, after further optimizations, can lead to an algorithm that shares the good performance of Zielonka’s algorithm on typical inputs, while reducing the worst-case complexity on difficult inputs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Parity games
  • Zielonka’s algorithm
  • quasi-polynomial time

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