Finding the Shortest Move-Sequence in the Graph-Generalized 15-Puzzle Is NP-Hard

  • Oded Goldreich

Abstract

Following Wilson (J. Comb. Th. (B), 1975), Johnson (J. of Alg., 1983), and Kornhauser, Miller and Spirakis (25th FOCS, 1984), we consider a game that consists of moving distinct pebbles along the edges of an undirected graph. At most one pebble may reside in each vertex at any time, and it is only allowed to move one pebble at a time (which means that the pebble must be moved to a previously empty vertex). We show that the problem of finding the shortest sequence of moves between two given “pebble configuations” is NP-Hard.

Keywords

NP-Completeness Games’ Complexity Computational Group Theory 

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References

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    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, p. 221. Freeman, San Francisco (1979)MATHGoogle Scholar
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    Johnson, D.S.: The NP-Completeness Column: An Ongoing Guide. J. of Algorithms 4, 397–411 (1983)MathSciNetCrossRefMATHGoogle Scholar
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    Kornhauser, D.M., Miller, G., Spirakis, P.: Coordinating Pebble Motion on Graphs, the Diameter of Permutation Groups, and Applications. In: Proc. of the 25th FOCS, pp. 241–250 (1984)Google Scholar
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    Wilson, R.W.: Graphs, Puzzles, Homotopy, and Alternating Groups. J. of Comb. Th. (B) 16, 86–96 (1974)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Oded Goldreich

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