Deciding parity games in quasipolynomial time

@article{Calude2017DecidingPG,
  title={Deciding parity games in quasipolynomial time},
  author={Cristian S. Calude and Sanjay Jain and Bakhadyr Khoussainov and Wei Li and Frank Stephan},
  journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2017}
}
It is shown that the parity game can be solved in quasipolynomial time. The parameterised parity game - with n nodes and m distinct values (aka colours or priorities) - 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(√n) to O(nlog(m)+6) and from an XP-algorithm with runtime O(nΘ(m)) for fixed parameter m to an FPT-algorithm with runtime O(n5)+g(m), for some function g depending on m only. As… 

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An ordered approach to solving parity games in quasi polynomial time and quasi linear space
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A first implementation for a quasi-polynomial algorithm is provided, and a number of side results are provided, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al.
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