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Simple Amazons Endgames and Their Connection to Hamilton Circuits in Cubic Subgrid Graphs

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Book cover Computers and Games (CG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2063))

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Abstract

Amazons is a young board game with simple rules and a high branching factor, which makes it a suitable test-bed for planning research. This paper considers the computational complexity of Amazons puzzles and restricted Amazons endgames. We first prove the NP-completeness of the Hamilton circuit problem for cubic subgraphs of the integer grid. This result is then used to showthat solving Amazons puzzles is an NP-complete task and determining the winner of simple Amazons endgames is NP-equivalent.

Acknowledgement

Many thanks to John Tromp who found an error in an earlier version of this paper.

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Author information

Authors and Affiliations

  1. NEC Research Institute, Princeton, NJ, 08540, USA

    Michael Buro

Authors
  1. Michael Buro
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Alberta, Edmonton, Alberta, Canada

    Tony Marsland

  2. Future University - Hakodate, Hakodate, Hokkaido, Japan

    Ian Frank

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© 2001 Springer-Verlag Berlin Heidelberg

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Buro, M. (2001). Simple Amazons Endgames and Their Connection to Hamilton Circuits in Cubic Subgrid Graphs. In: Marsland, T., Frank, I. (eds) Computers and Games. CG 2000. Lecture Notes in Computer Science, vol 2063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45579-5_17

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  • DOI: https://doi.org/10.1007/3-540-45579-5_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43080-3

  • Online ISBN: 978-3-540-45579-0

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