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Complexity results for the gap inequalities for the max-cut problem

Laura Galli (l.galli***at***unibo.it)
Konstantinos Kaparis (K.Kaparis***at***lancaster.ac.uk)
Adam N. Letchford (A.N.Letchford***at***lancaster.ac.uk)

Abstract: In 1996, Laurent and Poljak introduced an extremely general class of cutting planes for the max-cut problem, called gap inequalities. We prove several results about them, including the following: (i) there must exist non-dominated gap inequalities with gap larger than 1, unless NP = co-NP; (ii) there must exist non-dominated gap inequalities with exponentially large coefficients, unless NP = co-NP; (iii) the separation problem for gap inequalities can be solved in finite time (specifically, doubly exponential time).

Keywords: computational complexity, max-cut problem, cutting planes

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: L. Galli, K. Kaparis & A.N. Letchford (2012) Complexity results for the gap inequalities for the max-cut problem. Oper. Res. Lett., 40(3), 149-152.

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Entry Submitted: 07/19/2011
Entry Accepted: 07/19/2011
Entry Last Modified: 09/05/2012

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