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The Conjunction of Interval Among Constraints

  • Conference paper
Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems (CPAIOR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7298))

Abstract

An Among constraint holds if the number of variables that belong to a given value domain is between given bounds. This paper focuses on the case where the variable and value domains are intervals. We investigate the conjunction of Among constraints of this type. We prove that checking for satisfiability – and thus, enforcing bound consistency – can be done in polynomial time. The proof is based on a specific decomposition that can be used as such to filter inconsistent bounds from the variable domains. We show that this decomposition is incomparable with the natural conjunction of Among constraints, and that both decompositions do not ensure bound consistency. Still, experiments on randomly generated instances reveal the benefits of this new decomposition in practice. This paper also introduces a generalization of this problem to several dimensions and shows that satisfiability is \(\mathcal{R}\)-complete in the multi-dimensional case

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Authors and Affiliations

  1. TASC, Mines-Nantes, INRIA, LINA CNRS, 4, rue Alfred Kastler, 44300, Nantes, France

    Gilles Chabert & Sophie Demassey

Authors
  1. Gilles Chabert
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  2. Sophie Demassey
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Editors and Affiliations

  1. École des Mines de Nantes, 4, rue Alfred Kastler, 44307, Nantes Cedex 3, France

    Nicolas Beldiceanu

  2. École des Mines de Nantes, 4 rue Alfred Kastler, 44307, Nantes Cedex 3, France

    Narendra Jussien

  3. Institut de Mathématiques Appliquées, 44 rue Rabelais, 49008, Angers Cedex 01, France

    Éric Pinson

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© 2012 Springer-Verlag Berlin Heidelberg

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Chabert, G., Demassey, S. (2012). The Conjunction of Interval Among Constraints. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-29828-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29827-1

  • Online ISBN: 978-3-642-29828-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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