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An O(n log n) Bound Consistency Algorithm for the Conjunction of an alldifferent and an Inequality between a Sum of Variables and a Constant, and its Generalization

Nicolas Beldiceanu 1, * Mats Carlsson 2 Thierry Petit 1 Jean-Charles Régin 3, 4
* Corresponding author
1 TASC - Theory, Algorithms and Systems for Constraints
LINA - Laboratoire d'Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe CEP
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : This paper gives an O(nlog n) bound-consistency filtering algorithm for the conjunction alldifferent(V0,V1,...,Vn−1)∧ f(V0)⌖f(V1)⌖...⌖f(Vn−1)≤ cst, (V0,V1,...,Vn−1,cst∊ +), where (,⌖) is a commutative group, f is a unary function, and both ⌖ and f are monotone increasing. This complexity is equal to the complexity of the bound-consistency algorithm of the alldifferent constraint.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00754079
Contributor : Contraintes Lina <>
Submitted on : Tuesday, November 20, 2012 - 8:42:07 AM
Last modification on : Monday, October 12, 2020 - 10:30:31 AM

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Nicolas Beldiceanu, Mats Carlsson, Thierry Petit, Jean-Charles Régin. An O(n log n) Bound Consistency Algorithm for the Conjunction of an alldifferent and an Inequality between a Sum of Variables and a Constant, and its Generalization. 20th European Conference on Artificial Intelligence (ECAI'12), Aug 2012, Montpellier, France. pp.145-150, ⟨10.3233/978-1-61499-098-7-145⟩. ⟨hal-00754079⟩

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