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Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
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This paper studies the resolution of (augmented)weighted matching problems within a constraint programming (CP)framework. The first contribution of the paper is a set of techniquesthat improves substantially the performance of branch-and-boundalgorithms based on constraint propagation and the second contributionis the introduction of weighted matching as a global constraint( WeightedMatching), that can be propagated using specializedincremental algorithms from Operations Research. We first compareprogramming techniques that use constraint propagation with specializedalgorithms from Operations Research, such as the Busaker andGowen flow algorithm or the Hungarian method. Although CP isshown not to be competitive with specialized polynomial algorithmsfor ’’pure‘‘ matching problems, the situation is different assoon as the problems are modified with additional constraints.Using the previously mentioned set of techniques, a simpler branch-and-boundalgorithm based on constraint propagation can outperform a complexspecialized algorithm. These techniques have been applied withsuccess to the Traveling Salesman Problems [5], which can beseen as an augmented matching problem. We also show that an incrementalversion of the Hungarian method can be used to propagate a WeightedMatchingconstraint. This is an extension to the weighted case of thework of Régin [19], which we show to bring significantimprovements on a timetabling example.