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On the NP-hardness of deciding emptiness of the split closure of a rational polytope in the 0,1 hypercube

Dabeen Lee(dabeenl***at***andrew.cmu.edu)

Abstract: Split cuts are prominent general-purpose cutting planes in integer programming. The split closure of a rational polyhedron is what is obtained after intersecting the half-spaces defined by all the split cuts for the polyhedron. In this paper, we prove that deciding whether the split closure of a rational polytope is empty is NP-hard, even when the polytope is contained in the unit hypercube. As a direct corollary, we prove that optimization and separation over the split closure of a rational polytope in the unit hypercube are NP-hard, extending an earlier result of Caprara and Letchford.

Keywords: Integer programming, split closure, split cuts

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Integer Programming (0-1 Programming )

Citation: April 2018

Download: [PDF]

Entry Submitted: 08/07/2018
Entry Accepted: 08/07/2018
Entry Last Modified: 08/07/2018

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