New Deterministic Algorithms for Solving Parity Games

We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n−k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity games in time  kO(k)⋅O(n3), and general parity games in time (p+k)O(k)⋅O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k=o(n) this improves the previously fastest algorithm by Jurdziński, Paterson, and Zwick (SICOMP 2008).