Simple Extensions of Polytopes

  • Volker Kaibel
  • Matthias Walter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)


We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method to establish lower bounds on the simple extension complexity and show for several polytopes that they have large simple extension complexities. These examples include both the spanning tree and the perfect matching polytopes of complete graphs, uncapacitated flow polytopes for non-trivially decomposable directed acyclic graphs, and random 0/1-polytopes with vertex numbers within a certain range. On our way to obtain the result on perfect matching polytopes we improve on a result of Padberg and Rao’s on the adjacency structures of those polytopes.


Span Tree Complete Graph Directed Acyclic Graph Extended Formulation Simple Extension 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Volker Kaibel
    • 1
  • Matthias Walter
    • 1
  1. 1.Otto-von-Guericke Universität MagdeburgGermany

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