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

Author

Listed:
  • Hiroshi Nagamochi

    (Department of Information and Computer Science, Toyohashi)

  • Shigeki Katayama

    (Toshiba Corporation Power System & Service Company, Fuchu)

  • Toshihide Ibaraki

    (Kyoto University)

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.

Suggested Citation

  • Hiroshi Nagamochi & Shigeki Katayama & Toshihide Ibaraki, 2000. "A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 151-169, June.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:2:d:10.1023_a:1009804919645
    DOI: 10.1023/A:1009804919645
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    References listed on IDEAS

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    1. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
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