CONSTRUCTING CACTUS REPRESENTATION FOR ALL MINIMUM CUTS IN AN UNDIRECTED NETWORK
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概要
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The construction of a cactus representation for all minimum cuts in an edge-weighted, undirected network is studied in this paper. Given such a network with a set V of vertices and a set E of edges, the previously known algorithms for constructing a cactus representation require solving |V| - 1 maximum flow problems, each with a prescribed pair of source and sink, in order to find all minimum cuts that separate them. We first show that computing a maximum flow between a pair of vertices, s and t, reveals many other minimum cuts that do not separate s and t. Based on this fact, we propose a new algorithm that can choose an arbitrary pair of source and sink for each maximum flow problem. For a network with unit edge weights, our algorithm runs in O(|E| + λ|V|^2) time, where λ is the weight of a minimum cut.
- 社団法人日本オペレーションズ・リサーチ学会の論文
著者
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NAGAMOCHI Hiroshi
Department of Applied Mathematics and Physics, Kyoto University
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Nagamochi H
Kyoto Univ.
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Kameda Tiko
School of Computing Science Simon Fraser University
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Kameda Tiko
School Of Computing Science Faculty Of Applied Sciences Simon Fraser University
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Nagamochi Hiroshi
Department Of Applied Mathematics And Physics Graduate School Of Engineering Kyoto University
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