TY - JOUR

T1 - A new separation algorithm for the Boolean quadric and cut polytopes

AU - Letchford, Adam

AU - Sorensen, Michael M.

PY - 2014/8/2

Y1 - 2014/8/2

N2 - 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, ina 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.

AB - 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, ina 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.

KW - zero-one quadratic programming

KW - max-cut problem

KW - polyhedral combinatorics

KW - branch-and-cut

U2 - 10.1016/j.disopt.2014.07.002

DO - 10.1016/j.disopt.2014.07.002

M3 - Journal article

VL - 14

SP - 61

EP - 71

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

ER -