A Faster Algorithm for Solving One-Clock Priced Timed Games

Abstract

One-clock priced timed games is a class of two-player, zero-sum, continuous-time games that was defined and thoroughly studied in previous works. We show that one-clock priced timed games can be solved in time m 12ⁿ n ^O(1), where n is the number of states and m is the number of actions. The best previously known time bound for solving one-clock priced timed games was $2^{O(n^2+m)}$, due to Rutkowski. For our improvement, we introduce and study a new algorithm for solving one-clock priced timed games, based on the sweep-line technique from computational geometry and the strategy iteration paradigm from the algorithmic theory of Markov decision processes. As a corollary, we also improve the analysis of previous algorithms due to Bouyer, Cassez, Fleury, and Larsen; and Alur, Bernadsky, and Madhusudan.

Work supported by the Sino-Danish Center for the Theory of Interactive Computation, funded by the Danish National Research Foundation and the National Science Foundation of China (under the grant 61061130540). The authors acknowledge support from the Center for research in the Foundations of Electronic Markets (CFEM), supported by the Danish Strategic Research Council. Thomas Dueholm Hansen is a recipient of the Google Europe Fellowship in Game Theory, and this research is supported in part by this Google Fellowship; he was also supported in part by The Danish Council for Independent Research | Natural Sciences (grant no. 12-126512).