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.
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Bessiere, C., Hebrard, E., Hnich, B. et al. Filtering Algorithms for the NValue Constraint. Constraints 11, 271–293 (2006). https://doi.org/10.1007/s10601-006-9001-9
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DOI: https://doi.org/10.1007/s10601-006-9001-9