2023/04/29 by Paweł Parys, Parys, Paweł, Aleksander Wiącek +1 · 1 citation
Computer Science · #Artificial Intelligence in Games #Complexity and Algorithms in Graphs #Computer Science and Game Theory (cs.GT) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.2305.00308
openalex publication_date 2023/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We improve the complexity of solving parity games (with priorities in vertices) for d=ω(log n) by a factor of θ(d2): the best complexity known to date was O(mdn1.45+log2(d/log2(n))), while we obtain O(mn1.45+log2(d/log2(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 θ(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 to solve 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 θ(d).