Quadratic Convex Reformulation : a Computational Study of the Graph Bisection Problem
نویسندگان
چکیده
Given an undirected graph G = (V,E), we consider the graph bisection problem, which consists in partitioning the nodes of G in two disjoined sets with p and n− p nodes respectively such that the total weight of edges crossing between subsets is minimal. We apply QCR to it, a general method, presented in [4], which combines semidefinite programming (SDP) and Mixed Integer Quadratic Programming (MIQP). This method solves exactly general 0-1 quadratic programs (called (QP )) with linear constraints. It is composed of two phases : Phase I is devoted to reformulate (QP ) into a new problem, equivalent to (QP ), with a convex quadratic function; Phase II consists in submitting this new problem to a mixed-integer convex quadratic solver. Computational results reported in this paper show that the present approach is competitive with state-of-the-art methods for the graph bisection problem. Keyword : Quadratic 0-1 programming, Convex quadratic reformulation, Semidefinite programming, Graph bisection problem, Experiments.
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