A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs

Hiroshi Nagamochi (), Shigeki Katayama () and Toshihide Ibaraki ()
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Hiroshi Nagamochi: Department of Information and Computer Science, Toyohashi
Shigeki Katayama: Toshiba Corporation Power System & Service Company, Fuchu
Toshihide Ibaraki: Kyoto University

Journal of Combinatorial Optimization, 2000, vol. 4, issue 2, No 1, 169 pages

Abstract: Abstract For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(nk − 1F(n, m)) = O(mnk log (n2/m)) time, where F(n, m) denotes the time bound required to solve the maximum flow problem in G. The bounds Õ(mn5) for k = 5 and Õ(mn6) for k = 6 improve the previous best randomized bounds Õ(n8) and Õ(n10), respectively.

Keywords: minimum cuts; graphs; k-way cuts; polynomial algorithm (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1009804919645

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