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Engineering Branch-and-Cut Algorithms for the Equicut Problem

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Discrete Geometry and Optimization

Part of the book series: Fields Institute Communications ((FIC,volume 69))

Abstract

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such that the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefinite relaxations for the equicut problem, and find that linear bounds are competitive with the corresponding semidefinite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-and-cut algorithm has a better performance than the algorithm of Brunetta et al. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application.

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Acknowledgements

Financial support from the German Science Foundation is acknowledged under contract Li 1675/1. The first author acknowledges financial support from the Alexander von Humboldt Foundation and from the Natural Science and Engineering Research Council of Canada. We thank Helmut G. Katzgraber, Creighton Thomas and Juan Carlos Andersen for providing us with instances for the physics application.

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Authors and Affiliations

  1. Canada Research Chair in Discrete Nonlinear Optimization in Engineering, GERAD & École Polytechnique de Montréal, CP 6079, succ. Centre-ville, Montreal, QC, H3C 3A7, Canada

    Miguel F. Anjos

  2. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany

    Frauke Liers

  3. Institut für Informatik, Universität zu Köln, Weyertal 121, 50931, Köln, Germany

    Gregor Pardella & Andreas Schmutzer

Authors
  1. Miguel F. Anjos
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  2. Frauke Liers
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  3. Gregor Pardella
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  4. Andreas Schmutzer
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Corresponding author

Correspondence to Miguel F. Anjos .

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Editors and Affiliations

  1. , Mathematics & Statistics, University of Calgary, University Drive NW, Calgary, T2N 1N4, Alberta, Canada

    Karoly Bezdek

  2. , Department of Computing, McMaster University, Main Street West 1280, Hamilton, L8S 4K1, Ontario, Canada

    Antoine Deza

  3. School of Engineering, Department of Management Science and Eng, Stanford University, Via Ortega 475, Stanford, 94305, California, USA

    Yinyu Ye

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Anjos, M.F., Liers, F., Pardella, G., Schmutzer, A. (2013). Engineering Branch-and-Cut Algorithms for the Equicut Problem. In: Bezdek, K., Deza, A., Ye, Y. (eds) Discrete Geometry and Optimization. Fields Institute Communications, vol 69. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00200-2_2

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