# A faster deterministic exponential time algorithm for Energy Games and Mean Payoff Games

Dani Dorfman, Haim Kaplan, Uri Zwick

September, 2019

### 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(mnW, m 2^{n/2})), 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 ≥ 2^{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.

Publication

International Colloquium on Automata, Languages, and Programming (ICALP 2019)