Cardinality constraints and systems of restricted representatives

Ioannis Mourtos ()
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Ioannis Mourtos: Athens University of Economics and Business

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 9, 1089 pages

Abstract: 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.

Keywords: Global cardinality constraint; Polyhedral combinatorics; Constraint programming (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9810-5

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