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Weighted matching as a generic pruning technique applied to optimization constraints

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Abstract

We study the application of matching theory within a constraint programming framework. In this work we describe a filtering scheme based on weighted matchings. A first benefit of our pruning technique comes from the fact that it can be applied on various optimization constraints. In a number of important cases our method achieves domain consistency in polynomial time. A key feature in our implementation is the use of decomposition theory. The paper compares some of the optimization constraints reported in the literature and shows how they can be solved with the help of the weighted matching.

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Notes

  1. In terms of linear programming potentials are called dual variables and reduced weights are slacks.

  2. A bipartite graph \(G\) with bipartition \((V_1,V_2)\) is called convex on \(V_2\) if there exists an ordering of \(V_2\) so that for any \(x \in V_1\) the set \(\varGamma (x)\) forms an interval in the ordering.

  3. The diameter of a connected digraph is the maximal distance between two of its vertices.

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Acknowledgments

The author would like to thank the anonymous reviewers whose valuable comments and suggestions improved the presentation of this paper.

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  1. Augsburg, Germany

    Radosław Cymer

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  1. Radosław Cymer
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Cymer, R. Weighted matching as a generic pruning technique applied to optimization constraints. Ann Oper Res 217, 165–211 (2014). https://doi.org/10.1007/s10479-014-1582-x

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