Computing All Small Cuts in an Undirected Network

• Authors: Hiroshi Nagamochi;Kazuhiro Nishimura;Toshihide Ibaraki
• Venue: SIAM Journal on Discrete Mathematics
• Year: 1997

Let $\lambda({\cal N})$ denote the weight of a minimum cut in an edge-weighted undirected network ${\cal N}$, and $n$ and $m$ denote the numbers of vertices and edges, respectively. It is known that $O(n^{2k})$ is an upper bound on the number of cuts with weights less than $k\lambda({\cal N})$, where $k\geq 1$ is a given constant. This paper first shows that all cuts of weights less than $k\lambda({\cal N})$ can be enumerated in $O(m^2n+n^{2k}m)$ time without using the maximum flow algorithm. The paper then proves for $k