A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs

The cut packing problem in an undirected graph is to find a largest cardinality collection of pairwise edge-disjoint cuts. We provide the first experimental study of this NP-hard problem that is interesting from a pure theorist’s viewpoint as well as from the standpoint of scientific applications (e.g., in bioinformatics and network reliability). So far it could not be solved exactly. We propose a branch-price-and-cut algorithm to optimally solve instances from various graph classes, random and from the literature, with up to several hundred vertices. In particular, we investigate how complexity results match computational experience and how combinatorial properties help improve the algorithm’s performance.

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