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

Carlo Comin (1, 2) , Romeo Rizzi (3)

1 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 UNIVR | DI - Department of Computer Science [Verona]

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 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.

Mots clés: mean payoff games; value problem; optimal strategy synthesis; energy games; small energy-progress measures; pseudo-polynomial Time

Domaines: Informatique et théorie des jeux [cs.GT]; Algorithme et structure de données [cs.DS]

Carlo Comin, Romeo Rizzi. Improved Pseudo-polynomial Bound for the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games. Algorithmica, 2017, 77 (4), pp.995-1021. ⟨10.1007/s00453-016-0123-1⟩. ⟨hal-01577457⟩