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A Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Dani Dorfman, Haim Kaplan, Uri Zwick

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Author Details

Dani Dorfman
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Haim Kaplan
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Uri Zwick
  • Blavatnik School of Computer Science, Tel Aviv University, Israel

Funding

Haim Kaplan was partially supported by the Israel Science Foundation, grant 1841/14, by the German-Israeli Foundation for Scientific Research and Development, grant 1367/2017, and by the Blavatnik Research Foundation. Part of this research was carried out while Uri Zwick was visiting BARC, Copenhagen, funded by the VILLUM Foundation, grant 16582, and while he was visiting IRIF, Paris, with support from the FSMP.

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Dani Dorfman, Haim Kaplan, and Uri Zwick. A Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 114:1-114:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICALP.2019.114

Abstract

We present an improved exponential time algorithm for Energy Games, and hence also for Mean Payoff Games. The running time of the new algorithm is O (min(m n W, m n 2^{n/2} log W)), where n is the number of vertices, m is the number of edges, and when the edge weights are integers of absolute value at most W. For small values of W, the algorithm matches the performance of the pseudopolynomial time algorithm of Brim et al. on which it is based. For W >= n2^{n/2}, the new algorithm is faster than the algorithm of Brim et al. and is currently the fastest deterministic algorithm for Energy Games and Mean Payoff Games. The new algorithm is obtained by introducing a technique of forecasting repetitive actions performed by the algorithm of Brim et al., along with the use of an edge-weight scaling technique.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Stochastic games
Keywords
  • Energy Games
  • Mean Payoff Games
  • Scaling

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