The global cardinality constraint (gcc) [7], written as
$$ cardinality(x,J;l,u),x_{j}\in D_{j},j\in J, $$
states that each value d is received by at least l d and by at most u d of the variables {x j :j ∈ J}, where \(d\in D={\mathop{\textstyle \bigcup }}_{j\in J}D_{j}=\{0,\ldots ,|D|-1\};\) also, 0 ≤ l d  ≤ u d and u d  ≥ 1 for all d ∈ D. The gcc has several applications [2, 10], thus having been studied from the Constraint Programming community mainly for accomplishing various forms of consistency [4, 6–8] or for examining the tractability of a natural generalization [9].


Convex Hull Constraint Satisfaction Problem Facial Structure European Social Fund Identical Term 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ioannis Mourtos
    • 1
  1. 1.Department of Management Science and TechnologyAthens University of Economics and BusinessAthensGreece

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