A Simple Proof of a Minimum Cut Algorithm and Its Applications

Hiroshi NAGAMOCHI  Toshimasa ISHII  Toshihide IBARAKI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.10   pp.2231-2236
Publication Date: 1999/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
Keyword: 
graph,  edge-connectivity,  minimum cut,  flow,  MA-ordering,  dynamic tree structure,  

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Summary: 
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.