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Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts

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Algorithms and Computation (ISAAC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1741))

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Abstract

For an edge weighted undirected graph G and an integer k ≥ 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts.We show that the performance ratio of our algorithm is 2−3/k for an odd k and 2−(3k−4)/(k 2k) for an even k. The running time is O(kmn 3 log(n 2/m)) where n and m are the numbers of vertices and edges respectively.

This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The first author was also supported by the IBM Asia Fellowship Program.

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© 1999 Springer-Verlag Berlin Heidelberg

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Zhao, L., Nagamochi, H., Ibaraki, T. (1999). Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_38

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  • DOI: https://doi.org/10.1007/3-540-46632-0_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66916-6

  • Online ISBN: 978-3-540-46632-1

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