On the ESL algorithm for solving energy games

We propose a variant of an algorithm introduced by Schewe and also studied by Luttenberger for solving parity or mean-payoff games. We present it over energy games and call our variant the ESL algorithm (for Energy-Schewe-Luttenberger). We find that using potential reductions as introduced by Gurvich, Karzanov and Khachiyan allows for a simple and elegant presentation of the algorithm, which repeatedly applies a natural generalisation of Dijkstra's algorithm to the two-player setting due to Khachiyan, Gurvich and Zhao.