An Improved Pseudo-Polynomial Upper Bound for the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games

TL;DR

This paper presents a faster pseudo-polynomial algorithm for solving the Value Problem and Strategy Synthesis in Mean Payoff Games, improving previous bounds by a logarithmic factor through novel characterizations involving Energy Games.

Contribution

It introduces an $O(|V|^2 |E| W)$ algorithm that improves the pseudo-polynomial upper bound for mean payoff game solutions using new characterizations.

Findings

Faster pseudo-polynomial algorithm with improved bounds

Characterization of values via reweighted Energy Games

Enhanced strategy synthesis methods

Abstract

In this work we offer an $O(|V|^2 |E|\, W)$ pseudo-polynomial time deterministic algorithm for solving the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games. This improves by a factor $\log(|V|\, W)$ the best previously known pseudo-polynomial time upper bound due to Brim,~\etal The improvement hinges on a suitable characterization of values, and a description of optimal positional strategies, in terms of reweighted Energy Games and Small Energy-Progress Measures.