Abstract
Sudoku is a notorious logic-based puzzle that is popular with puzzle enthusiasts the world over. From a computational perspective, Sudoku is also a problem that belongs to the set of NP-complete problems, implying that we cannot hope to find a polynomially bounded algorithm for solving the problem in general. Considering this feature, in this paper we demonstrate how a metaheuristic-based method for solving Sudoku puzzles (which was reported by the same author in an earlier paper), can actually be significantly improved if it is coupled with Constraint Programming techniques. Our results, which have been gained through a large amount of empirical work, suggest that this combination of techniques results in a hybrid algorithm that is significantly more powerful than either of its constituent parts.
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References
van Hoeve, W.J.: The alldifferent constraint: A survey. CoRR cs.PL/0105015 (2001)
Simonis, H.: Sudoku as a constraint problem. In: Hnich, B., Prosser, P., Smith, B. (eds.) Proc. 4th Int. Works. Modelling and Reformulating Constraint Satisfaction Problems, pp. 13–27 (2005)
Yato, T., Seta, T.: Complexity and completeness of finding another solution and its application to puzzles. IEICE Trans. Fundamentals EA6-A(5), 1052–1060 (2003)
Lewis, R.: In press: Metaheuristics can solve sudoku puzzles. Journal of heuristics 13 (2007)
Smith, B.: Phase transitions and the mushy region in constraint satisfaction problems. In: Cohn, A. (ed.) 11th European Conference on Artificial Intelligence, pp. 100–104. John Wiley and Sons ltd., Chichester (1994)
Turner, J.S.: Almost all k-colorable graphs are easy to color. Journal of Algorithms 9, 63–82 (1988)
Felgenhauer, B., Jarvis, F.: Mathematics of sudoku. Online Resource: (2006), http://www.afjarvis.staff.shef.ac.uk/sudoku/
Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: IJCAI-1991. Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, Sidney, Australia, pp. 331–337 (1991)
van Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Dordrecht (1987)
Mepham, M.: Sudoku archive. Online (2006), http://www.sudoku.org.uk/backpuzzles.htm
Royle, G.: Minimum sudoku. Online (2006), http://www.csse.uwa.edu.au/~gordon/sudokumin.php
Hanssen, V.: Sudoku puzzles. Online (2006), http://www.menneske.no/sudoku/eng/
Armstrong, S.: Sudoku solving techniques. Online (2006), http://www.sadmansoftware.com/sudoku/techniques.htm
Jensen, T.R., Toft, B.: Graph Coloring Problems, 1st edn. Wiley-Interscience, Chichester (1994)
Burke, E.K., De Causmaecker, P. (eds.): PATAT 2002. LNCS, vol. 2740. Springer, Heidelberg (2003)
Duong, T.A., Lam, K.H.: Combining constraint programming and simulated annealing on university exam timetabling. In: RIVF2004. Proceedings of the 2nd International Conference in Computer Sciences, Research, Innovation & Vision for the Future, pp. 205–210 (2004)
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Lewis, R. (2007). On the Combination of Constraint Programming and Stochastic Search: The Sudoku Case. In: Bartz-Beielstein, T., et al. Hybrid Metaheuristics. HM 2007. Lecture Notes in Computer Science, vol 4771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75514-2_8
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DOI: https://doi.org/10.1007/978-3-540-75514-2_8
Publisher Name: Springer, Berlin, Heidelberg
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