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A new separation algorithm for the Boolean quadric and cut polytopes

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<mark>Journal publication date</mark>2/08/2014
<mark>Journal</mark>Discrete Optimization
Volume14
Number of pages11
Pages (from-to)61-71
Publication statusPublished
Original languageEnglish

Abstract

A separation algorithm is a procedure for generating cutting planes. Up to now, only a few polynomial-time separation algorithms were known for the Boolean quadric and cut polytopes. These polytopes arise in connection with zero-one quadratic programming and the maxcut problem, respectively. We present a new algorithm, which separates over a class of valid inequalities that includes all odd bicycle wheel inequalities and (2p + 1, 2)-circulant inequalities. It exploits, in
a non-trivial way, three known results in the literature: one on the separation of {0,1/2}-cuts, one on the symmetries of the polytopes in question, and one on an affine mapping between the polytopes.