On the relative strength of split, triangle and quadrilateral cuts

Authors:
Amitabh Basu;Pierre Bonami;Gérard Cornuéjols;François Margot
Affiliations:
Carnegie Mellon University;Université de Marseille, France;Carnegie Mellon University;Carnegie Mellon University
Venue:
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Year:
2009

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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.