Mathematical Programming

, Volume 154, Issue 1–2, pp 273–303 | Cite as

Reverse split rank

  • Michele Conforti
  • Alberto Del Pia
  • Marco Di Summa
  • Yuri Faenza
Full Length Paper Series B
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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.

Keywords

Integer programming Cutting planes Split inequalities Split rank Integer hull 

Mathematics Subject Classification

90C10 
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Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015

Authors and Affiliations

  • Michele Conforti
    • 1
  • Alberto Del Pia
    • 2
  • Marco Di Summa
    • 1
  • Yuri Faenza
    • 3
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PadovaPaduaItaly
  2. 2.Department of Industrial and Systems Engineering, Wisconsin Institute for DiscoveryUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.DISOPT, Institut de Mathématiques d’analyse et ApplicationsEPFLLausanneSwitzerland

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