A Recursive Approach to Solving Parity Games in Quasipolynomial Time

Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zie...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 18, Issue 1; no. 1; pp. 8:1 - 8:18
Main Authors:	Lehtinen, Karoliina, Parys, Paweł, Schewe, Sven, Wojtczak, Dominik
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 01.01.2022 Logical Methods in Computer Science e.V
Subjects:	Computer Science computer science - computer science and game theory computer science - formal languages and automata theory
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zielonka's classic algorithm that brings its complexity down to $n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-18(1:8)2022