Computing all small cuts in undirected networks

Abstract

Let λ(N) denote the wof a minimum cut in an edgeweighted undirected network N, where n and m are the numbers of vertices and edges, respectively. It is known that O(n2k) is an upper bound on the number of cuts with weights less than kλ(N). We first show that all cuts of weights less than kλ(N) can be enumerated in O(mn3 + n2k+2) time without using the maximum flow algorithm. We then prove for k < 4/3 that (2) is a tight upper bound on the number of cuts of weights less than kλ(N).