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Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

Faster Algorithm for Turn-based Stochastic Games with Bounded Treewidth

Abstract

Turn-based stochastic games (aka simple stochastic games) are two-player zero-sum games played on directed graphs with probabilistic transitions. The goal of player-max is to maximize the probability to reach a target state against the adversarial player-min. These games lie in NP ∩ coNP and are among the rare combinatorial problems that belong to this complexity class for which the existence of polynomial-time algorithm is a major open question. While randomized sub-exponential time algorithm exists, all known deterministic algorithms require exponential time in the worst-case. An important open question has been whether faster algorithms can be obtained parametrized by the treewidth of the game graph. Even deterministic sub-exponential time algorithm for constant treewidth turn-based stochastic games has remain elusive. In this work our main result is a deterministic algorithm to solve turn-based stochastic games that, given a game with n states, treewidth at most t, and the bit-complexity of the probabilistic transition function log D, has running time O ((tn2 log D)t log n). In particular, our algorithm is quasi-polynomial time for games with constant or poly-logarithmic treewidth.

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Information

Published In

cover image Proceedings
Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
Pages: 4590 - 4605
Editors: Nikhil Bansal, University of Michigan, Ann Arbor, Michigan, USA and Viswanath Nagarajan, University of Michigan, Ann Arbor, Michigan, USA
ISBN (Online): 978-1-61197-755-4

History

Published online: 16 January 2023

Authors

Affiliations

Krishnendu Chatterjee
1∗Institute of Science and Technology Austria.
Tobias Meggendorfer
1∗Institute of Science and Technology Austria.
Raimundo Saona
1∗Institute of Science and Technology Austria.
Jakub Svoboda
1∗Institute of Science and Technology Austria.

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