ISAAC 1994: Algorithms and Computation pp 190-198

# Computing all small cuts in undirected networks

• Hiroshi Nagamochi
• Kazuhiro Nishimura
• Toshihide Ibaraki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)

## Abstract

Let λ(N) denote the weight of a minimum cut in an edge-weighted 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 n ) is a tight upper bound on the number of cuts of weights less than kλ(N).

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