Enumeration of 2-Level Polytopes

  • Adam Bohn
  • Yuri Faenza
  • Samuel Fiorini
  • Vissarion Fisikopoulos
  • Marco Macchia
  • Kanstantsin Pashkovich
Conference paper

DOI: 10.1007/978-3-662-48350-3_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)
Cite this paper as:
Bohn A., Faenza Y., Fiorini S., Fisikopoulos V., Macchia M., Pashkovich K. (2015) Enumeration of 2-Level Polytopes. In: Bansal N., Finocchi I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science, vol 9294. Springer, Berlin, Heidelberg

Abstract

We propose the first algorithm for enumerating all combinatorial types of 2-level polytopes of a given dimension d, and provide complete experimental results for \(d \leqslant 6\). Our approach is based on the notion of a simplicial core, that allows us to reduce the problem to the enumeration of the closed sets of a discrete closure operator, along with some convex hull computations and isomorphism tests.

Keywords

Polyhedral computation Optimization Formal concept analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Adam Bohn
    • 1
  • Yuri Faenza
    • 2
  • Samuel Fiorini
    • 1
  • Vissarion Fisikopoulos
    • 1
  • Marco Macchia
    • 1
  • Kanstantsin Pashkovich
    • 3
  1. 1.Université libre de BruxellesBrusselsBelgium
  2. 2.Ecole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  3. 3.C & O DepartmentUniversity of WaterlooWaterlooCanada

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