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Reverse Split Rank

  • Conference paper
Integer Programming and Combinatorial Optimization (IPCO 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8494))

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Abstract

The reverse split rank of an integral polytope P is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is P. Already in ℝ3 there exist polytopes with infinite reverse split rank. We give a geometric characterization of the integral polytopes in ℝn with infinite reverse split rank.

This work was supported by the Progetto di Eccellenza 2008–2009 of Fondazione Cassa di Risparmio di Padova e Rovigo. Yuri Faenza’s research was supported by the German Research Foundation (DFG) within the Priority Programme 1307 Algorithm Engineering.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Italy

    Michele Conforti & Marco Di Summa

  2. Business Analytics and Mathematical Sciences Department, IBM Watson Research Center, Yorktown Heights, NY, USA

    Alberto Del Pia

  3. DISOPT, Institut de mathématiques d’analyse et applications, EPFL, Switzerland

    Yuri Faenza

Authors
  1. Michele Conforti
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  2. Alberto Del Pia
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  3. Marco Di Summa
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  4. Yuri Faenza
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Editor information

Editors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, Beal Avenue, 1205, Ann Arbor, MI, USA

    Jon Lee

  2. Research Institute for Discrete Mathematics, University of Bonn, Lennéstr. 2, P.O. Box, 53113, Bonn, Germany

    Jens Vygen

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Conforti, M., Del Pia, A., Di Summa, M., Faenza, Y. (2014). Reverse Split Rank. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_20

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  • DOI: https://doi.org/10.1007/978-3-319-07557-0_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07556-3

  • Online ISBN: 978-3-319-07557-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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