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Parity Games of Bounded Tree-Depth

Author Konrad Staniszewski

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ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Parity Games
  • Circuits
  • Tree-Depth
  • Clique-Width

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Abstract

The exact complexity of solving parity games is a major open problem. Several authors have searched for efficient algorithms over specific classes of graphs. In particular, Obdržálek showed that for graphs of bounded tree-width or clique-width, the problem is in P, which was later improved by Ganardi, who showed that it is even in LOGCFL (with an additional assumption for clique-width case). Here we extend this line of research by showing that for graphs of bounded tree-depth the problem of solving parity games is in logspace uniform AC⁰. We achieve this by first considering a parameter that we obtain from a modification of clique-width, which we call shallow clique-width. We subsequently provide a suitable reduction.

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Konrad Staniszewski. Parity Games of Bounded Tree-Depth. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CSL.2023.33

Author Details

Konrad Staniszewski
  • University of Warsaw, Poland
  • IDEAS NCBR Sp. z o.o., Warsaw, Poland

Funding

  • Staniszewski, Konrad: Work supported by the National Science Centre, Poland (grant no. 2021/41/B/ST6/03914).

Acknowledgements

I want to thank the supervisor of my master’s thesis Damian Niwiński and anonymous reviewers for valuable feedback.

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