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Split rank of triangle and quadrilateral inequalities


  • DEY, Santanu S.

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

  • LOUVEAUX, Quentin

    () (Montefiore Institute, Université de Liège, Belgium)


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," CORE Discussion Papers 2009055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2009055

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    mixed integer programs; split rank; group relaxations;

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