Graphs and Combinatorics

, Volume 32, Issue 5, pp 1931–1944

Extended Formulations for Independence Polytopes of Regular Matroids

  • Volker Kaibel
  • Jon Lee
  • Matthias Walter
  • Stefan Weltge
Original Paper
  • 94 Downloads

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.

Keywords

Extended formulation Independence polytope Regular matroid Decomposition 

Mathematics Subject Classification

52Bxx 

Copyright information

© Springer Japan 2016

Authors and Affiliations

  • Volker Kaibel
    • 1
  • Jon Lee
    • 2
  • Matthias Walter
    • 1
  • Stefan Weltge
    • 1
  1. 1.Institut für Mathematische Optimierung, Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Department of Industrial and Operations EngineeringThe University of MichiganAnn ArborUSA

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