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On the Relative Strength of Split, Triangle and Quadrilateral Cuts

Amitabh Basu(abasu1***at***andrew.cmu.edu)
Pierre Bonami(pierre.bonami***at***lif.univ-mrs.fr)
Gerard Cornuejols(gc0v***at***andrew.cmu.edu)
Francois Margot(fmargot***at***andrew.cmu.edu)

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.

Keywords: Mixed integer programming, split closure, 2-row cuts

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Combinatorial Optimization (Polyhedra )

Category 3: Integer Programming (Cutting Plane Approaches )

Citation: Tepper Working Paper 2008 E-38, Tepper School of Business, Carnegie Mellon University (7/2008)

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Entry Submitted: 08/03/2008
Entry Accepted: 08/03/2008
Entry Last Modified: 08/03/2008

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