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

Abstract

In this work we offer an $$O(|V|^2 |E|\, W)$$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 $$\log (|V|\, W)$$log(|V|W) the best previously known pseudo-polynomial time upper bound due to Brim et al. 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.