Parameterized Algorithms for Parity Games

Abstract : Determining the winner of a Parity Game is a major problem in computational complexity with a number of applications in verification. In a parameterized complexity setting, the problem has often been considered with parameters such as (directed versions of) treewidth or clique-width, by applying dynamic programming techniques.In this paper we adopt a parameterized approach which is more inspired by well-known (non-parameterized) algorithms for this problem. We consider a number of natural parameterizations, such as by Directed Feedback Vertex Set, Distance to Tournament, and Modular Width. We show that, for these parameters, it is possible to obtain recursive parameterized algorithms which are simpler, faster and only require polynomial space. We complement these results with some algorithmic lower bounds which, among others, rule out a possible avenue for improving the best-known sub-exponential time algorithm for parity games.
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Jakub Gajarsky, Michail Lampis, Kazuhisa Makino, Valia Mitsou, Sebastian Ordyniak. Parameterized Algorithms for Parity Games. 40th International Symposium, MFCS 2015, Aug 2015, Milan, Italy. pp.336-347, ⟨10.1007/978-3-662-48054-0_28⟩. ⟨hal-01326881⟩

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