Deciding parity games in quasipolynomial time.
STOC(2017)
摘要
It is shown that the parity game can be solved in quasipolynomial time. The parameterised parity game â with n nodes and m distinct values (aka colours or priorities) â is proven to be in the class of fixed parameter tractable (FPT) problems when parameterised over m. Both results improve known bounds, from runtime nO(ân) to O(nlog(m)+6) and from an XP-algorithm with runtime O(nÎ(m)) for fixed parameter m to an FPT-algorithm with runtime O(n5)+g(m), for some function g depending on m only. As an application it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n)c), for any c, unless FPT = W[1].
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关键词
Parity Games,Muller Games,Quasipolynomial Time Algorithm
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