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 of arbitrary k.
report 2017-040, RWTH Aachen University, November 2017