Revisiting the Sequence Constraint
Many combinatorial problems, such as car sequencing and rostering, feature sequence constraints, restricting the number of occurrences of certain values in every subsequence of a given width. To date, none of the filtering algorithms proposed guaranteed domain consistency. In this paper, we present three filtering algorithms for the sequence constraint, with complementary strengths. One borrows ideas from dynamic programming; another reformulates it as a regular constraint; the last is customized. The last two algorithms establish domain consistency. Our customized algorithm does so in polynomial time, and can even be applied to a generalized sequence constraint for subsequences of variable widths. Experimental results show the practical usefulness of each.
KeywordsCardinality Constraint Local Graph Sequence Constraint Knapsack Constraint Goal Vertex
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- 3.Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global Constraint Catalog. Technical Report T2005-08, SICS (2005)Google Scholar
- 5.Demassey, S., Pesant, G., Rousseau, L.-M.: A cost-regular based hybrid column generation approach. Constraints (under final review)Google Scholar
- 6.Mohr, R., Masini, G.: Good Old Discrete Relaxation. In: European Conference on Artificial Intelligence (ECAI), pp. 651–656 (1988)Google Scholar
- 8.Régin, J.-C.: Generalized Arc Consistency for Global Cardinality Constraint. In: AAAI/IAAI, pp. 209–215. AAAI Press/The MIT Press (1996)Google Scholar
- 10.Régin, J.-C., Puget, J.-F.: A Filtering Algorithm for Global Sequencing Constraints. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 32–46. Springer, Heidelberg (1997)Google Scholar