A Simple Proof of a Minimum Cut Algorithm and Its Applications

Abstract

For the correctness of the minimum cut algorithm proposed in [H. Nagamochi and T. Ibaraki, Computing edge-connectivity of multigraphs and capacitated graphs, SIAM J. Discrete Mathematics, 5, 1992, pp. 54–66], several simple proofs have been presented so far. This paper gives yet another simple proof. As a byproduct, it can provide an O(m log n) time algorithm that outputs a maximum flow between the pair of vertices s and t selected by the algorithm, where n and m are the numbers of vertices and edges, respectively. This algorithm can be used to speed up the algorithm to compute DAGs,t that represents all minimum cuts separating vertices s and t in a graph G, and the algorithm to compute the cactus Γ(G) that represents all minimum cuts in G. key words: graph, edge-connectivity, minimum cut, flow, MAordering, dynamic tree structure

Cite this paper

@inproceedings{Nagamochi1996ASP, title={A Simple Proof of a Minimum Cut Algorithm and Its Applications}, author={Hiroshi Nagamochi and Toshimasa Ishii}, year={1996} }