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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 12nnO(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.

A Faster Algorithm for Solving One-Clock Priced Timed Games