Abstract
Parity games are a much researched class of games in NP ∩ CoNP that are not known to be in P. Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small. In this paper, we show that, if a tree decomposition is provided, then parity games with bounded treewidth can be solved in O(k 3k + 2 ·n 2 ·(d + 1)3k) time, where n, k, and d are the size, treewidth, and number of priorities in the parity game. This significantly improves over previously best algorithm, given by Obdržálek, which runs in \(O(n \cdot d^{2(k+1)^2})\) time. Our techniques can also be adapted to show that the problem lies in the complexity class NC2, which is the class of problems that can be efficiently parallelized. This is in stark contrast to the general parity game problem, which is known to be P-hard, and thus unlikely to be contained in NC.
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Fearnley, J., Schewe, S. (2012). Time and Parallelizability Results for Parity Games with Bounded Treewidth. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_20
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DOI: https://doi.org/10.1007/978-3-642-31585-5_20
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