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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 interested theorists and practitioners alike. 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 howdoi:10.1145/2851492 fatcat:y6majvyrhrdevlw3k3akboidw4