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Lower bounds on the lattice-free rank for packing and covering integer programs

Merve Bodur(bodur***at***mie.utoronto.ca)
Alberto Del Pia(delpia***at***wisc.edu)
Santanu S. Dey(santanu.dey***at***isye.gatech.edu)
Marco Molinaro(mmolinaro***at***inf.puc-rio.br)

Abstract: In this paper, we present lower bounds on the rank of the split closure, the multi-branch closure and the lattice-free closure for packing sets as a function of the integrality gap. We also provide a similar lower bound on the split rank of covering polyhedra. These results indicate that whenever the integrality gap is high, these classes of cutting planes must necessarily be applied for many rounds in order to obtain the integer hull.

Keywords: Integer programming, packing, covering, split rank, multi-branch split rank, lattice-free rank

Category 1: Integer Programming

Category 2: Integer Programming (Cutting Plane Approaches )

Citation:

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Entry Submitted: 09/29/2017
Entry Accepted: 09/29/2017
Entry Last Modified: 09/29/2017

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