Filtering algorithms for the NVALUE constraint

Authors:
Christian Bessiere;Emmanuel Hebrard;Brahim Hnich;Zeynep Kiziltan;Toby Walsh
Affiliations:
LIRMM, CNRS/University of Montpellier, France;NICTA and UNSW, Sydney, Australia;4C and UCC, Cork, Ireland;University of Bologna, Italy;NICTA and UNSW, Sydney, Australia
Venue:
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2005

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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.