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.
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Nagamochi, H., Katayama, S. & Ibaraki, T. A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs. Journal of Combinatorial Optimization 4, 151–169 (2000). https://doi.org/10.1023/A:1009804919645
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DOI: https://doi.org/10.1023/A:1009804919645