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Cardinality constraints and systems of restricted representatives

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  • Ioannis Mourtos

    (Athens University of Economics and Business)

Abstract

Cardinality constraints have received considerable attention from the Constraint Programming community as (so-called) global constraints that appear in the formulation of several real-life problems, while also having an interesting combinatorial structure. After discussing the relation of cardinality constraints with well-known combinatorial problems (e.g., systems of restricted representatives), we study the polytope defined by the convex hull of vectors satisfying two such constraints, in the case where all variables share a common domain. We provide families of facet-defining inequalities that are polytime separable, together with a condition for when these families of inequalities define a convex hull relaxation. Our results also hold for the case of a single such constraint.

Suggested Citation

  • Ioannis Mourtos, 2016. "Cardinality constraints and systems of restricted representatives," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1061-1089, April.
  • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9810-5
    DOI: 10.1007/s10878-014-9810-5
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    References listed on IDEAS

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    1. H.P. Williams & Hong Yan, 2001. "Representations of the all_different Predicate of Constraint Satisfaction in Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 96-103, May.
    2. Michela Milano & Greger Ottosson & Philippe Refalo & Erlendur S. Thorsteinsson, 2002. "The Role of Integer Programming Techniques in Constraint Programming's Global Constraints," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 387-402, November.
    3. BALAS, Egon & BOCKMAYR, Alexander & PISARUK, Nicolai & WOLSEY, Laurence, 2002. "On unions and dominants of polytopes," LIDAM Discussion Papers CORE 2002008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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