Abstract
We study the global cardinality constraint (gcc) and propose an O(n 1.5 d) algorithm for domain consistency and an O(cn + dn) algorithm for range consistency where n is the number of variables, d the number of values in the domain, and c an output dependent variable smaller than or equal to n. We show how to prune the cardinality variables in O(n 2 d + n 2.66) steps, detect if gcc is universal in constant time and prove that it is NP-Hard to maintain domain consistency on extended-GCC.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications, 1st edn. Prentice Hall, Englewood Cliffs (1993)
Hall, P.: On representatives of subsets. J. of the London Mathematical Society, 26–30 (1935)
Hopcroft, J., Karp, R.: n 52 algorithm for maximum matchings in bipartite graphs. SIAM Journal of Computing 2, 225–231
ILOG S. A. ILOG Solver 4.2 user’s manual (1998)
Quimper, C.-G., van Beek, P., López-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); Extended Report CS-2003-10
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)
Leconte, M.: A bounds-based reduction scheme for constraints of difference. In: The Constraint 1996 Int’l. Workshop on Constraint-Based Reasoning, pp. 19–28 (1996)
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)
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)
Stergiou, K., Walsh, T.: The difference all-difference makes. In: IJCAI 1999, pp. 414–419 (1999)
Tarjan, R.: Depth-first search and linear graph algorithms. SIAM Journal of Computing 1, 146–160
Van Hentenryck, P., Michel, L., Perron, L., Régin, J.-C.: Constraint programming in OPL. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 98–116. Springer, Heidelberg (1999)
Van Hentenryck, P., Simonis, H., Dincbas, M.: Constraint satisfaction using constraint logic programming. Artificial Intelligence 58, 113–159 (1992)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Quimper, CG., López-Ortiz, A., van Beek, P., Golynski, A. (2004). Improved Algorithms for the Global Cardinality Constraint. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_40
Download citation
DOI: https://doi.org/10.1007/978-3-540-30201-8_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
Online ISBN: 978-3-540-30201-8
eBook Packages: Springer Book Archive