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Gallai-Edmonds decomposition as a pruning technique

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Abstract

We introduce a generic propagation mechanism for constraint programming. The method is based on the results of matching theory which is a mature and well-studied subject of graph theory. A first benefit of our new pruning technique comes from the fact that it can be applied on several global constraints whose solution is representable by a matching in a particular graph. In this work we describe a filtering scheme for such a family based on the Gallai-Edmonds Structure Theorem. In a number of important cases our method achieves hyper-arc consistency in polynomial time.

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Notes

  1. A barrier is a set \(X \subseteq V\) such that the number of odd components of \(G-X\) is equal to \(|X| + \delta (G)\).

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Acknowledgments

The author would like to thank the referees for many useful suggestions.

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  1. Augsburg, Germany

    Radosław Cymer

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  1. Radosław Cymer
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Correspondence to Radosław Cymer.

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Cymer, R. Gallai-Edmonds decomposition as a pruning technique. Cent Eur J Oper Res 23, 149–185 (2015). https://doi.org/10.1007/s10100-013-0309-4

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