FORMULATIONS AND VALID INEQUALITIES FOR THE NODE CAPACITATED GRAPH PARTITIONING PROBLEM

We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of th e edges between the subsets of the partition. This problem has a varie ty of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations f or this problem and discuss the links between these formulations. Havi ng chosen to work in the space of edges of the multicut, we investigat e the convex hull of incidence vectors of feasible multicuts. In parti cular, several classes of inequalities are introduced, and their stren gth and robustness are analyzed as various problem parameters change.