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A note on the split rank of intersection cuts

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Abstract

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that \({\lceil \log_2 (l)\rceil}\) is a lower bound on the split rank of the intersection cut, where l is the number of integer points lying on the boundary of the restricted lattice-free set satisfying the condition that no two points lie on the same facet of the restricted lattice-free set. The use of this result is illustrated by obtaining a lower bound of \({\lceil \log_2( n+1) \rceil}\) on the split rank of n-row mixing inequalities.

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  1. CORE, Université catholique de Louvain, Louvain, Belgium

    Santanu S. Dey

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Correspondence to Santanu S. Dey.

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This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.

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Dey, S.S. A note on the split rank of intersection cuts. Math. Program. 130, 107–124 (2011). https://doi.org/10.1007/s10107-009-0329-y

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