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

  • Michael Buro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2063)


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.


Amazons endgame puzzle NP-complete planning 


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  1. 1.
    M. Buro. How machines have learned to play Othello. IEEE Intelligent Systems J.,14(6):12–14, 1999.Google Scholar
  2. 2.
    J. Culberson. Sokoban is PSPACE-complete. In Proceedings in Informatics 4, pages 65–76. arleton Scientific,Waterloo, Canada, 1999.Google Scholar
  3. 3.
    D. DeCoste. The significance of Kasparov versus Deep Blue and the future of computer chess. ICCA J., 21(1):33–43, 1998.Google Scholar
  4. 4.
    G.W. Flake and E.B. Baum. RushHour is PSPACE-complete, or why you should generously tip parking lot attendants. to appear in TCS, 2000.Google Scholar
  5. 5.
    M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman and Company NewYork, 1979.zbMATHGoogle Scholar
  6. 6.
    A. Itai, C.H. Papadimitriou, and J.L. Szwarcfiter. Hamilton paths in grid graphs. SIAM J. Comput., 11(4):676–686, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Kant. Drawing planar graphs using the canonical ordering. Algorithmica, 16(1):4–32, 1996.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Korf. Finding optimal solutions to Rubik’s cube using pattern databases. Fourteenth National Conference on Artificial Intelligence Ninth Innovative Applications of Artificial Intelligence Conference, pages 700–705, 1997.Google Scholar
  9. 9.
    M. Müller. Computer Go: A research agenda. ICCA Journal, 22(2):104–112, 1999.Google Scholar
  10. 10.
    J. Plesnik. The NP-completeness of the Hamiltonian cycle problem in planar digraphs with degree bound two. Information Processing Letters, 8(4):199–201, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    J. Schaeffer. One Jump Ahead: Challenging Human Supremacy in Checkers. SpringerVerlag, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michael Buro
    • 1
  1. 1.NEC Research InstitutePrincetonUSA

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