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International Symposium on Mathematical Foundations of Computer Science

MFCS 2009: Mathematical Foundations of Computer Science 2009 pp 675–686Cite as

From Parity and Payoff Games to Linear Programming

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

Abstract

This paper establishes a surprising reduction from parity and mean payoff games to linear programming problems. While such a connection is trivial for solitary games, it is surprising for two player games, because the players have opposing objectives, whose natural translations into an optimisation problem are minimisation and maximisation, respectively. Our reduction to linear programming circumvents the need for concurrent minimisation and maximisation by replacing one of them, the maximisation, by approximation. The resulting optimisation problem can be translated to a linear programme by a simple space transformation, which is inexpensive in the unit cost model, but results in an exponential growth of the coefficients. The discovered connection opens up unexpected applications – like μ-calculus model checking – of linear programming in the unit cost model, and thus turns the intriguing academic problem of finding a polynomial time algorithm for linear programming in this model of computation (and subsequently a strongly polynomial algorithm) into a problem of paramount practical importance: All advancements in this area can immediately be applied to accelerate solving parity and payoff games, or to improve their complexity analysis.

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Authors and Affiliations

  1. University of Liverpool, UK

    Sven Schewe

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  1. Sven Schewe
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Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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Schewe, S. (2009). From Parity and Payoff Games to Linear Programming. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_57

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

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