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 $k^{ O(\sqrt{ k})}\cdot O(n^3)$, and general parity games in time $(p+k)^{ O(\sqrt{ k})} \cdot O(pnm)$, 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 Jurdzi{ \'n}ski, Paterson, and Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree.
Categories: cs.CC cs.DS