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Playing Games with Algorithms: Algorithmic Combinatorial Game Theory

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Mathematical Foundations of Computer Science 2001 (MFCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in combinatorial game theory, which analyzes ideal play in perfect-information games. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Erik D. Demaine

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  1. Erik D. Demaine
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Editors and Affiliations

  1. Mathematical Institute, AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Sgall

  2. Faculty of Mathematics and Physics Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Aleš Pultr  & Petr Kolman  & 

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Demaine, E.D. (2001). Playing Games with Algorithms: Algorithmic Combinatorial Game Theory. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_3

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  • DOI: https://doi.org/10.1007/3-540-44683-4_3

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  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

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