A decomposition algorithm for multi-terminal networks flows

AbstractFor any large network N with n vertices and O(n2) edges, the direct approach treats the network as a whole and takes O(n4) time to find the maximum flow values between all pairs of vertices. A large network can sometimes be divided into tri-connected component. In this paper, a decomposition algorithm is introduced to take advantage of the situation. For any network N which has n vertices, O(n2) edges and p tri-connected components, with approximately equal numbers of vertices in each component, the decomposition algorithm required O(n4/p3+n2) time to compute the (2n) maximum flow values, an improvement over the O(n4) time direct approach