Theoretical Computer Science
Minimum-Cost Reachability for Priced Timed Automata
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Optimal Paths in Weighted Timed Automata
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Optimal-Reachability and Control for Acyclic Weighted Timed Automata
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Geometric intersection problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction
Theory of Computing Systems
Improved undecidability results on weighted timed automata
Information Processing Letters
Almost optimal strategies in one clock priced timed games
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Optimal strategies in priced timed game automata
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Reachability-time games on timed automata
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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.