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A new separation algorithm for the Boolean quadric and cut polytopes. (English) Zbl 1308.90209
Summary: 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 max-cut 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 \(\{0,\frac{1}{2}\}\)-cuts, one on the symmetries of the polytopes in question, and one on an affine mapping between the polytopes.

MSC:
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C20 Quadratic programming
90C09 Boolean programming
Software:
Concorde; BiqMac
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