Bipartition of a graph with minimal cost

The problem considered is that of partitioning a arc-weighted graph into two parts, each of which constrained in size, in order to minimize the sum of the costs of the cut arcs. After formulating this problem as a 0.1 guadratic program, the authors calculated a lower bound by using Lagrangian relaxation. The best Lagrangian multiplier is determined in at most n-1 applications of a maximum flow algorithm to a network with n+2 vertices and n+m arcs, where n and m denote the number of vertices and arcs in the initial graph. A Branch and Bound algorithm using this result is presented and computational experience shows that an optimal solution is obtained within quite reasonable times which are much less than for the exact methods known up to now.