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Extended Formulations for Independence Polytopes of Regular Matroids

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Abstract

We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin’s extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour’s decomposition theorem for regular matroids. As a consequence, the extended formulations can be computed in polynomial time.

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Change history

  • 16 December 2019

    We report a logical error in our article that turns out to be fatal for the main result. The error lies in Lemma 3 for the case of a 3-sum, that is

  • 16 December 2019

    We report a logical error in our article that turns out to be fatal for the main result. The error lies in Lemma 3 for the case of a 3-sum, that is

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Acknowledgments

We would like to thank Klaus Truemper for valuable comments on the decomposition of matroids.

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Authors and Affiliations

  1. Institut für Mathematische Optimierung, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Volker Kaibel, Matthias Walter & Stefan Weltge

  2. Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109-2117, USA

    Jon Lee

Authors
  1. Volker Kaibel
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  2. Jon Lee
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  3. Matthias Walter
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  4. Stefan Weltge
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Corresponding author

Correspondence to Stefan Weltge.

Additional information

V. Kaibel and S. Weltge acknowledge support by Deutsche Forschungsgemeinschaft (KA 1616/4-1). J. Lee was partially supported by NSF grant CMMI–1160915 and ONR grant N00014-14-1-0315.

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Kaibel, V., Lee, J., Walter, M. et al. Extended Formulations for Independence Polytopes of Regular Matroids. Graphs and Combinatorics 32, 1931–1944 (2016). https://doi.org/10.1007/s00373-016-1709-8

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  • DOI: https://doi.org/10.1007/s00373-016-1709-8

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