Peter Austin, Daniele Dell'Erba

An improved exponential time algorithm for Energy Games and Mean Payoff Games has been recently proposed in ICALP 19. The new algorithm prevents some of the repetitive operations performed by the classic value iteration algorithm of Brim et al., leading to an approach with time complexity $O(\min(mnW,mn2^{n/2}\log W))$. Unfortunately, the pseudo-code of the algorithm includes inaccuracies that violate two Lemmata used in the correctness and complexity proofs. In this technical report, we describe the problems, propose a fixed version of the algorithm, and correct the proofs for the Lemmata.