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Cardinality constraints and systems of restricted representatives


  • Ioannis Mourtos

    (Athens University of Economics and Business)


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

    1. 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.
    2. 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).
    3. John N. Hooker, 2012. "Integrated Methods for Optimization," International Series in Operations Research and Management Science, Springer, number 978-1-4614-1900-6, December.
    4. 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.
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