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Symmetric Cardinality Constraint with Costs


Publication Type:

Report - MRTC




The symmetric cardinality constraint is described in terms of a set of variables X=<x_1,<,x_k>, which take their values as subsets of V=<v_1,<,v_n>. It constraints the cardinality of the set assigned to each variable to be in an interval [l_{x_i},u_{x_i}] and at the same time it restricts the number of occurrences of each value v_j in V in the sets assigned to variables in X to be in an other interval [l_{v_j},u_{v_j}]. In this paper we extend the symmetric cardinality constraint with a function which associate with each value of each variable a cost and constraints the global cost of the constraint to the sum of costs associated with assigned values. We also give an algorithm for computing the consistency of a symmetric cardinality constraint with costs and describe filtering methods for this constraint.


author = {Waldemar Kocjan and Bj{\"o}rn Lisper},
title = {Symmetric Cardinality Constraint with Costs},
number = {ISSN 1404-3041 ISRN MDH-MRTC-167/2005-1-SE},
month = {December},
year = {2004},
url = {}