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On the relative strength of split, triangle and quadrilateral cuts

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Abstract

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Amitabh Basu, Gérard Cornuéjols & François Margot

  2. LIF, Faculté des Sciences de Luminy, Université de Marseille, Marseille, France

    Pierre Bonami & Gérard Cornuéjols

Authors
  1. Amitabh Basu
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  2. Pierre Bonami
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  3. Gérard Cornuéjols
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  4. François Margot
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Correspondence to Amitabh Basu.

Additional information

A. Basu was supported by a Mellon Fellowship, P. Bonami was supported by ANR grant BLAN06-1-138894, G. Cornuéjols was supported by NSF grant CMMI0653419, ONR grant N00014-97-1-0196 and ANR grant BLAN06-1-138894, and F. Margot was supported by ONR grant N00014-97-1-0196.

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Basu, A., Bonami, P., Cornuéjols, G. et al. On the relative strength of split, triangle and quadrilateral cuts. Math. Program. 126, 281–314 (2011). https://doi.org/10.1007/s10107-009-0281-x

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  • DOI: https://doi.org/10.1007/s10107-009-0281-x

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