Filtering Algorithms for the NValue Constraint

Authors:
Christian Bessiere;Emmanuel Hebrard;Brahim Hnich;Zeynep Kiziltan;Toby Walsh
Affiliations:
LIRMM-CNRS, Montpellier, France 34392;National ICT Australia Ltd, The University of New South Wales, Sydney, Australia 1466;Izmir University of Economics, Izmir, Turkey 35330 balcova;University of Bologna, Bologna, Italy 40136;National ICT Australia Ltd, The University of New South Wales, Sydney, Australia 1466
Venue:
Constraints
Year:
2006

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Abstract

The NValue constraint 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.