Abstract
We study decompositions of the global NValue constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NValue which decomposition can simulate with the same time complexity but with a much greater space complexity. This suggests that the benefit of a global propagator may often not be in saving time but in saving space. Our other theoretical contribution is to show for the first time that range consistency can be enforced on NValue with the same worst-case time complexity as bound consistency. Finally, the decompositions we study are readily encoded as linear inequalities. We are therefore able to use them in integer linear programs.
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References
Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proc. of the 12th National Conf. on AI, pp. 362–367. AAAI, Menlo Park (1994)
Leconte, M.: A bounds-based reduction scheme for constraints of difference. In: Proc. of 2nd Int. Workshop on Constraint-Based Reasoning, Constraint 1996 (1996)
Puget, J.: A fast algorithm for the bound consistency of alldiff constraints. In: 15th National Conf. on Artificial Intelligence, pp. 359–366. AAAI, Menlo Park (1998)
Bessiere, C., Hentenryck, P.V.: To be or not to be... a global constraint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 789–794. Springer, Heidelberg (2003)
Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, C.G., Walsh, T.: Decompositions of all different, global cardinality and related constraints. In: Proc. of 21st IJCAI, pp. 419–424 (2009)
Bessiere, C., Katsirelos, G., Narodytska, N., Walsh, T.: Circuit complexity and decompositions of global constraints. In: Proc. of 21st IJCAI, pp. 412–418 (2009)
Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of global constraints. In: Proc. of the 19th National Conf. on AI. AAAI, Menlo Park (2004)
Pachet, F., Roy, P.: Automatic generation of music programs. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 331–345. Springer, Heidelberg (1999)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Filtering algorithms for the NVALUE constraint. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 79–93. Springer, Heidelberg (2005)
Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of global constraints. Constraints 12, 239–259 (2007)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Quimper, C.G., Walsh, T.: The parameterized complexity of global constraints. In: Proc. of the 23rd National Conf. on AI, pp. 235–240. AAAI, Menlo Park (2008)
Beldiceanu, N.: Pruning for the minimum constraint family and for the number of distinct values constraint family. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 211–224. Springer, Heidelberg (2001)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Filtering algorithms for the NVALUE constraint. Constraints 11, 271–293 (2006)
Stergiou, K., Walsh, T.: The difference all-difference makes. In: Proc. of 16th IJCAI (1999)
Östergård, P., Weakley, W.: Values of domination numbers of the queen’s graph. The Electronic Journal of Combinatorics 8 (2001)
Ohrimenko, O., Stuckey, P., Codish, M.: Propagation = lazy clause generation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 544–558. Springer, Heidelberg (2007)
Beldiceanu, N., Carlsson, M., Debruyne, R., Petit, T.: Reformulation of Global Constraints Based on Constraints Checkers. Constraints 10, 339–362 (2005)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: The range and roots constraints: Specifying counting and occurrence problems. In: Proc. of 19th IJCAI, pp. 60–65 (2005)
Quimper, C.G., Walsh, T.: Global grammar constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 751–755. Springer, Heidelberg (2006)
Quimper, C.G., Walsh, T.: Decomposing global grammar constraints. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 590–604. Springer, Heidelberg (2007)
Brand, S., Narodytska, N., Quimper, C.G., Stuckey, P., Walsh, T.: Encodings of the Sequence Constraint. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 210–224. Springer, Heidelberg (2007)
van Hoeve, W.J., Pesant, G., Rousseau, L.M., Sabharwal, A.: Revisiting the Sequence Constraint. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 620–634. Springer, Heidelberg (2006)
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Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, CG., Walsh, T. (2010). Decomposition of the NValue Constraint. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_12
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DOI: https://doi.org/10.1007/978-3-642-15396-9_12
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