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SIAM Journal on Computing
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Deciding the winner in parity games is in UP ∩ co-UP
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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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 nO(k2) time and nO(k2) space, where k is the tree-width of the graph that the game is played on. This paper presents an algorithm that uses nO(k 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).