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#### Cost-filtering Algorithms for the two Sides of the Sum of Weights of Distinct Values Constraint

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##### Zitation

Beldiceanu, N., Carlsson, M., & Thiel, S.(2002). *Cost-filtering
Algorithms for the two Sides of the Sum of Weights of Distinct Values Constraint* (SICS-T-2002:14-SE). Uppsala,
Sweden: Swedish Institute of Computer Science.

Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0019-EBAD-A

##### Zusammenfassung

This article introduces the sum of weights of distinct values
constraint, which can be seen as a generalization of the number of
distinct values as well as of the alldifferent, and the relaxed
alldifferent constraints. This constraint holds if a cost variable is
equal to the sum of the weights associated to the distinct values taken
by a given set of variables. For the first aspect, which is related to
domination, we present four filtering algorithms. Two of them lead to
perfect pruning when each domain variable consists of one set of
consecutive values, while the two others take advantage of holes in the
domains. For the second aspect, which is connected to maximum matching
in a bipartite graph, we provide a complete filtering algorithm for the
general case. Finally we introduce several generic deduction rules,
which link both aspects of the constraint. These rules can be applied to
other optimization constraints such as the minimum weight alldifferent
constraint or the global cardinality constraint with costs. They also
allow taking into account external constraints for getting enhanced
bounds for the cost variable. In practice, the sum of weights of
distinct values constraint occurs in assignment problems where using a
resource once or several times costs the same. It also captures
domination problems where one has to select a set of vertices in order
to control every vertex of a graph.