Faster algorithm for turn-based stochastic games with bounded treewidth

Chatterjee K, Meggendorfer T, Saona Urmeneta RJ, Svoboda J. 2023. Faster algorithm for turn-based stochastic games with bounded treewidth. Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 4590–4605.

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Conference Paper | Published | English
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.
Publishing Year
Date Published
2023-02-01
Proceedings Title
Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms
Acknowledgement
This research was partially supported by the ERC CoG 863818 (ForM-SMArt) grant.
Page
4590-4605
Conference
SODA: Symposium on Discrete Algorithms
Conference Location
Florence, Italy
Conference Date
2023-01-22 – 2023-01-25
IST-REx-ID

Cite this

Chatterjee K, Meggendorfer T, Saona Urmeneta RJ, Svoboda J. Faster algorithm for turn-based stochastic games with bounded treewidth. In: Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2023:4590-4605. doi:10.1137/1.9781611977554.ch173
Chatterjee, K., Meggendorfer, T., Saona Urmeneta, R. J., & Svoboda, J. (2023). Faster algorithm for turn-based stochastic games with bounded treewidth. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 4590–4605). Florence, Italy: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977554.ch173
Chatterjee, Krishnendu, Tobias Meggendorfer, Raimundo J Saona Urmeneta, and Jakub Svoboda. “Faster Algorithm for Turn-Based Stochastic Games with Bounded Treewidth.” In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, 4590–4605. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/1.9781611977554.ch173.
K. Chatterjee, T. Meggendorfer, R. J. Saona Urmeneta, and J. Svoboda, “Faster algorithm for turn-based stochastic games with bounded treewidth,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, Florence, Italy, 2023, pp. 4590–4605.
Chatterjee K, Meggendorfer T, Saona Urmeneta RJ, Svoboda J. 2023. Faster algorithm for turn-based stochastic games with bounded treewidth. Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 4590–4605.
Chatterjee, Krishnendu, et al. “Faster Algorithm for Turn-Based Stochastic Games with Bounded Treewidth.” Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2023, pp. 4590–605, doi:10.1137/1.9781611977554.ch173.
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