conference paper
An O(n2) time algorithm for alternating Büchi games
published
yes
Krishnendu
Chatterjee
author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X
Monika
Henzinger
author
KrCh
department
SODA: Symposium on Discrete Algorithms
Modern Graph Algorithmic Techniques in Formal Verification
project
Quantitative Graph Games: Theory and Applications
project
Rigorous Systems Engineering
project
Microsoft Research Faculty Fellowship
project
Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is Õ(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n·m) boundary by presenting a new technique that reduces the running time to O(n 2). This bound also leads to O(n 2) time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n 3)), and (3) in Markov decision processes (improving for m > n 4/3 an earlier bound of O(min(m 1.5, m·n 2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n 2), which is an improvement over earlier bounds for m > n 4/3. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem.
SIAM2012Kyoto, Japan
eng
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms10.1137/1.9781611973099.109
1386 - 1399
https://research-explorer.app.ist.ac.at/record/2141 https://research-explorer.app.ist.ac.at/record/5379
K. Chatterjee, M. Henzinger, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2012, pp. 1386–1399.
K. Chatterjee and M. Henzinger, “An O(n2) time algorithm for alternating Büchi games,” in <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Kyoto, Japan, 2012, pp. 1386–1399.
Chatterjee, K., & Henzinger, M. (2012). An O(n2) time algorithm for alternating Büchi games. In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 1386–1399). Kyoto, Japan: SIAM. <a href="https://doi.org/10.1137/1.9781611973099.109">https://doi.org/10.1137/1.9781611973099.109</a>
Chatterjee, Krishnendu, and Monika Henzinger. “An O(N2) Time Algorithm for Alternating Büchi Games.” In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 1386–99. SIAM, 2012. <a href="https://doi.org/10.1137/1.9781611973099.109">https://doi.org/10.1137/1.9781611973099.109</a>.
Chatterjee, Krishnendu, and Monika Henzinger. “An O(N2) Time Algorithm for Alternating Büchi Games.” <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, SIAM, 2012, pp. 1386–99, doi:<a href="https://doi.org/10.1137/1.9781611973099.109">10.1137/1.9781611973099.109</a>.
Chatterjee K, Henzinger M. An O(n2) time algorithm for alternating Büchi games. In: <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>. SIAM; 2012:1386-1399. doi:<a href="https://doi.org/10.1137/1.9781611973099.109">10.1137/1.9781611973099.109</a>
Chatterjee K, Henzinger M. 2012. An O(n2) time algorithm for alternating Büchi games. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 1386–1399.
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