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Enumeration of 2-Level Polytopes

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Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

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.

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Author information

Authors and Affiliations

  1. Université libre de Bruxelles, Brussels, Belgium

    Adam Bohn, Samuel Fiorini, Vissarion Fisikopoulos & Marco Macchia

  2. Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Yuri Faenza

  3. C & O Department, University of Waterloo, Waterloo, Canada

    Kanstantsin Pashkovich

Authors
  1. Adam Bohn
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  2. Yuri Faenza
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  3. Samuel Fiorini
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  4. Vissarion Fisikopoulos
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  5. Marco Macchia
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  6. Kanstantsin Pashkovich
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Corresponding author

Correspondence to Adam Bohn .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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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. https://doi.org/10.1007/978-3-662-48350-3_17

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

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