Abstract

Determining the winner of a Parity Game is a major problem in com-putational 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 in-spired 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 param-eterized 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. 1