Solving simple stochastic games with few coin toss positions

Authors:
Rasmus Ibsen-Jensen;Peter Bro Miltersen
Affiliations:
Department of Computer Science, Aarhus University, Denmark;Department of Computer Science, Aarhus University, Denmark
Venue:
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Year:
2012

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Abstract

Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r! n) where n is the number of positions of the simple stochastic game and r is the number of its coin toss positions. Chatterjee et al. pointed out that a variant of strategy iteration can be implemented to solve this problem in time 4rnO(1). In this paper, we show that an algorithm combining value iteration with retrograde analysis achieves a time bound of O(r 2r (r logr+n)), thus improving both time bounds. We also improve the analysis of Chatterjee et al. and show that their algorithm in fact has complexity 2rnO(1).