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arXiv · 1406.5433

The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average

Xavier Allamigeon·Pascal Benchimol·Stéphane Gaubert
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Abstract

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a tropical analogue of the shadow-vertex simplex algorithm, which solves mean payoff games via linear feasibility problems over the tropical semiring $(\mathbb{R} \cup \{-\infty\}, \max, +)$. The key ingredient in our approach is that the shadow-vertex pivoting rule can be transferred to tropical polyhedra, and that its computation reduces to optimal assignment problems through Pl\"ucker relations.

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Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert. 2014-06-20. The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average. https://doi.org/10.1007/978-3-662-43948-7_8

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