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

  • Michael Bastubbe
  • Marco E. LübbeckeEmail author
Full Length Paper

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 \(k=\infty \).

Keywords

Hypergraph Balanced vertex separator Matrix decomposition Integer programming 

Mathematics Subject Classification

90C27 90C09 49M27 

Notes

Supplementary material

12532_2019_171_MOESM1_ESM.pdf (486 kb)
Supplementary material 1 (pdf 485 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.Lehrstuhl für Operations Research, RWTH Aachen UniversityAachenGermany

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