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Filtering Algorithms for the NValue Constraint

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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00106098
Contributor : Christine Carvalho de Matos <>
Submitted on : Friday, October 13, 2006 - 10:23:10 AM
Last modification on : Saturday, October 12, 2019 - 5:24:45 PM

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Christian Bessière, Emmanuel Hébrard, Brahim Hnich, Zeynep Kiziltan, Toby Walsh. Filtering Algorithms for the NValue Constraint. CPAIOR, May 2005, Prague, Czech Republic. pp.79-93, ⟨10.1007/11493853_8⟩. ⟨lirmm-00106098⟩

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