Minimal Cost Cut Equivalent Networks

This paper is concerned with the following problem in network synthesis. Suppose that we are given a network with real-valued capacities on each arc. There is a cost associated with each arc which is proportional to the magnitude of the arc capacity. We wish to determine new arc capacities such that the capacity of each cut in the new network differs from the capacity of the corresponding cut in the original network by a specified constant and such that the total cost is minimized. This problem is shown to be equivalent to solving a minimum cost flow problem on a related network.