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The Tropical Shadow-Vertex Algorithm Solves Mean Payoff Games in Polynomial Time on Average

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Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8572))

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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 (ℝ ∪ { − ∞ }, 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 Plücker relations.

X. Allamigeon and S. Gaubert are partially supported by the PGMO program of EDF and Fondation Mathématique Jacques Hadamard. P. Benchimol is supported by a PhD fellowship of DGA and École Polytechnique.

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Authors and Affiliations

  1. INRIA and CMAP, École Polytechnique, CNRS, France

    Xavier Allamigeon, Pascal Benchimol & Stéphane Gaubert

Authors
  1. Xavier Allamigeon
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  2. Pascal Benchimol
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  3. Stéphane Gaubert
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Elias Koutsoupias

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Allamigeon, X., Benchimol, P., Gaubert, S. (2014). The Tropical Shadow-Vertex Algorithm Solves Mean Payoff Games in Polynomial Time on Average. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_8

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  • DOI: https://doi.org/10.1007/978-3-662-43948-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43947-0

  • Online ISBN: 978-3-662-43948-7

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