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 k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root 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 Jurdzinski, Paterson, and Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. (C) 2018 Elsevier B.V. All rights reserved