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Split rank of triangle and quadrilateral inequalities

Author

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  • DEY, Santanu S.

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • LOUVEAUX, Quentin

    (Montefiore Institute, Université de Liège, Belgium)

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 et al. [2] and Cornu´ejols and Margot [13] 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 et al. [12], 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 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.

Suggested Citation

  • DEY, Santanu S. & LOUVEAUX, Quentin, 2009. "Split rank of triangle and quadrilateral inequalities," LIDAM Discussion Papers CORE 2009055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2009055
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2009.html
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    Cited by:

    1. Gennadiy Averkov & Christian Wagner & Robert Weismantel, 2011. "Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 721-742, November.

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