Abstract
The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NP-hard. We show that computing even the lower bound on the number of values is NP-hard. We therefore study different approximation heuristics for this problem. We introduce three new methods for computing a lower bound on the number of values. The first two are based on the maximum independent set problem and are incomparable to a previous approach based on intervals. The last method is a linear relaxation of the problem. This gives a tighter lower bound than all other methods, but at a greater asymptotic cost.
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References
Beldiceanu, N.: Pruning for the minimum constraint family and for the Number of Distinct Values. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, p. 211. Springer, Heidelberg (2001)
Beldiceanu, N., Carlsson, M., Thiel, S.: Cost-Filtering Algorithms for the two sides of the Sum of Weights of Distinct Values Constraint. SICS technical report (2002)
Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of global constraints. In: Proceedings AAAI 2004 (2004)
Roy, P., Pachet, F.: Automatic generation of music programs. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 331–345. Springer, Heidelberg (1999)
Shahar, S., Even, G., Rawitz, D.: Hitting sets when the vc-dimension is small (2004) (submitted to a journal publication)
Halldórsson, M., Radhakrishnan, J.: Greed is good: Approximating independent sets in sparse and bounded-degree graphs. In: Proceedings STOC 1994, pp. 439–448 (1994)
Paschos, V.T., Demange, M.: Improved approximations for maximum independent set via approximation chains. Appl. Math. Lett. 10, 105–110 (1997)
Marzewski, E.: Sur deux propriétés des classes s’ensembles. Fund. Math. 33, 303–307 (1945)
Johnson, D.S., Garey, M.R.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman and Company, New York (1979)
Petit, T., Regin, J.C., Bessiere, C.: Specific filtering algorithms for over-constrained problems. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 451–463. Springer, Heidelberg (2001)
Debruyne, R., Bessiere, C.: Some practicable filtering techniques for the constraint satisfaction problem. In: Proceedings IJCAI 1997 (1997)
Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings AAAI 1994, pp. 362–367 (1994)
Turán, P.: On an extremal problem in graph theory. In: Mat. Fiz. Lapok (in Hungarian), pp. 48, 436–452 (1941)
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Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T. (2005). Filtering Algorithms for the NValue Constraint. 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_8
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DOI: https://doi.org/10.1007/11493853_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26152-0
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