Split Rank of Triangle and Quadrilateral Inequalities

Authors:
Santanu S. Dey;Quentin Louveaux
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;Department of Electrical Engineering and Computer Science, Montefiore Institute, University of Liège, 4000 Liege, Belgium
Venue:
Mathematics of Operations Research
Year:
2011

Citing 28
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Abstract

A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and Cornuéjols and Margot showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. From an example given by Cook et al. it is known that one particular class of facet-defining triangle inequality does not have finite split rank. In this paper we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank.