Mathematical Programming Computation, Volume 12, Issue 1, March 2020

A branch-and-price algorithm for capacitated hypergraph vertex separation

Michael Bastubbe, Marco E. Lübbecke

We exactly solve the 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=∞.

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