Split rank of triangle and quadrilateral inequalities
Abstract
A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen, Louveaux, Weismantel and Wolsey (2007) and Cornuejols and Margot (2008) showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook, Kannan and Schrijver (1990), it is known that one particular class of facet-defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have a finite split-rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.
Cite
@article{arxiv.0906.0887,
title = {Split rank of triangle and quadrilateral inequalities},
author = {Santanu Dey and Quentin Louveaux},
journal= {arXiv preprint arXiv:0906.0887},
year = {2009}
}
Comments
39 pages and 13 figures