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Reverse split rank

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Abstract

The reverse split rank of an integral polyhedron \(P\) is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is \(P\). Already in \(\mathbb {R}^3\) there exist polyhedra with infinite reverse split rank. We give a geometric characterization of the integral polyhedra in \(\mathbb {R}^n\) with infinite reverse split rank.

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Acknowledgments

Michele Conforti and Marco Di Summa acknowledge support from the Univesity of Padova (grant “Progetto di Ateneo 2013”). Yuri Faenza’s research was supported by the German Research Foundation (DFG) within the Priority Programme 1307 Algorithm Engineering. The authors are grateful to two anonymous referees, whose detailed comments helped us to improve the paper.

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Authors and Affiliations

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

    Michele Conforti & Marco Di Summa

  2. Department of Industrial and Systems Engineering, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, USA

    Alberto Del Pia

  3. DISOPT, Institut de Mathématiques d’analyse et Applications, EPFL, Lausanne, 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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Correspondence to Marco Di Summa.

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Conforti, M., Del Pia, A., Di Summa, M. et al. Reverse split rank. Math. Program. 154, 273–303 (2015). https://doi.org/10.1007/s10107-015-0883-4

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