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Decomposition of the NValue Constraint

Abstract : We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a much greater space complexity. This suggests that the benefit of a global propagator may often not be in saving time but in saving space. Our other theoretical contribution is to show for the first time that range consistency can be enforced on NVALUE with the same worst-case time complexity as bound consistency. Finally, the decompositions we study are readily encoded as linear inequalities. We are therefore able to use them in integer linear programs.
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Christian Bessière, George Katsirelos, Nina Narodytska, Claude-Guy Quimper, Toby Walsh. Decomposition of the NValue Constraint. CP: Principles and Practice of Constraint Programming, Sep 2010, St. Andrews, Scotland, United Kingdom. pp.114-128, ⟨10.1007/978-3-642-15396-9_12⟩. ⟨lirmm-00558048⟩

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