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- W4384788699 abstract "We improve the complexity of solving parity games (with priorities in vertices) for $$d=omega (log n)$$ by a factor of $$varTheta (d^2)$$ : the best complexity known to date was $$mathcal {O}(mdn^{1{.}45+log _2(d/log _2 n)})$$ , while we obtain $$mathcal {O}(mn^{1{.}45+log _2(d/log _2 n)}/d)$$ , where n is the number of vertices, m is the number of edges, and d is the number of priorities. We base our work on existing algorithms using universal trees, and we improve their complexity. We present two independent improvements. First, an improvement by a factor of $$varTheta (d)$$ comes from a more careful analysis of the width of universal trees. Second, we perform (or rather recall) a finer analysis of requirements for a universal tree: while for solving games with priorities on edges one needs an n-universal tree, in the case of games with priorities in vertices it is enough to use an n/2-universal tree. This way, we allow solving games of size 2n in the time needed previously to solve games of size n; such a change divides the quasi-polynomial complexity again by a factor of $$varTheta (d)$$ ." @default.
- W4384788699 created "2023-07-20" @default.
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- W4384788699 date "2023-01-01" @default.
- W4384788699 modified "2023-09-26" @default.
- W4384788699 title "Improved Complexity Analysis of Quasi-Polynomial Algorithms Solving Parity Games" @default.
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- W4384788699 doi "https://doi.org/10.1007/978-3-031-36978-0_22" @default.
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