Parity Games on Graphs with Medium Tree-Width

This paper studies the problem of solving parity games on graphs with bounded tree-width. Previous work by Obdržálek has produced an algorithm that uses n ) time and n ) space, where k is the tree-width of the graph that the game is played on. This paper presents an algorithm that uses n log n) time and O(n+ k log n) space. This is the fastest known algorithm for parity games whose tree-width k satisfies (in standard asymptotic notation) k ∈ ω(log n) and k ∈ o(√n/ log n).