Errata to: "Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games"

TL;DR

This paper corrects inaccuracies in a previously proposed exponential time algorithm for Energy and Mean Payoff Games, providing a fixed version and corrected proofs to ensure its correctness and complexity bounds.

Contribution

It identifies errors in the original algorithm's pseudo-code, proposes fixes, and revises the proofs to validate the improved algorithm's correctness.

Findings

Corrected pseudo-code for the algorithm

Validated the algorithm's correctness with revised proofs

Confirmed the improved time complexity bounds

Abstract

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.