Abstract
We exactly solve the \({\mathcal {NP}}\)-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit in preprocessing. We perform an extensive computational study, in particular on hypergraphs coming from the application of re-arranging a matrix into single-bordered block-diagonal form. Our experimental results show that our proposal complements the previous exact approaches in terms of applicability for larger k, and significantly outperforms them in the case \(k=\infty \).
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Bastubbe, M., Lübbecke, M.E. A branch-and-price algorithm for capacitated hypergraph vertex separation. Math. Prog. Comp. 12, 39–68 (2020). https://doi.org/10.1007/s12532-019-00171-5
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DOI: https://doi.org/10.1007/s12532-019-00171-5