Abstract
We propose a natural generalization of arc-consistency, which we call multiconsistency: A value v in the domain of a variable x is k-multiconsistent with respect to a constraint C if there are at least k solutions to C in which x is assigned the value v. We present algorithms that determine which variable-value pairs are k-multiconsistent with respect to several well known global constraints. In addition, we show that finding super solutions is strictly harder than finding arbitrary solutions and suggest multiconsistency as an alternative way to search for robust solutions.
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References
Apt, K.R.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)
Beldiceanu, N., Katriel, I., Thiel, S.: Filtering algorithms for the Same constraint. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 65–79. Springer, Heidelberg (2004)
Bleuzen-Guernalec, N., Colmerauer, A.: Optimal narrowing of a block of sortings in optimal time. Constraints 5(1-2), 85–118 (2000)
Fukuda, K., Matsui, T.: Finding all the perfect matchings in bipartite graphs. Appl. Math. Lett. 7(1), 15–18 (1994)
Hebrard, E., Hnich, B., Walsh, T.: Super solutions in constraint programming. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 157–172. Springer, Heidelberg (2004)
Hopcroft, J.E., Karp, R.M.: An n 5/2 algorithm for maximum matching in bipartite graphs. SIAM J. Computing 2(4), 225–231 (1973)
Katriel, I., Thiel, S.: Fast bound consistency for the global cardinality constraint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 437–451. Springer, Heidelberg (2003)
Lopez-Ortiz, A., Quimper, C.-G., Tromp, J., van Beek, P.: A fast and simple algorithm for bounds consistency of the alldifferent constraint. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (2003)
Mehlhorn, K., Thiel, S.: Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 306–319. Springer, Heidelberg (2000)
Puget, J.-F.: A fast algorithm for the bound consistency of alldiff constraints. In: Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence, July 1998, pp. 359–366 (1998)
Quimper, C.-G., López-Ortiz, A., van Beek, P., Golynski, A.: Improved algorithms for the global cardinality constraint. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 542–556. Springer, Heidelberg (2004)
Quimper, C.-G., van Beek, P., Lopez-Ortiz, A., Golynski, A., Sadjad, S.B.: An efficient bounds consistency algorithm for the global cardinality constraint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 600–614. Springer, Heidelberg (2003)
Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: AAAI 1994, pp. 362–367 (1994)
Régin, J.-C.: Generalized Arc-Consistency for Global Cardinality Constraint. In: AAAI 1996, pp. 209–215 (1996)
van Hoeve, W.J.: The alldifferent constraint: A survey (2001) (manuscript)
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Elbassioni, K., Katriel, I. (2005). Multiconsistency and Robustness with Global Constraints. In: Barták, R., Milano, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493853_14
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DOI: https://doi.org/10.1007/11493853_14
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