IEEJ Transactions on Electronics, Information and Systems
Online ISSN : 1348-8155
Print ISSN : 0385-4221
ISSN-L : 0385-4221
A New Approximate Algorithm for the Minimum k-Cut Problem by Using Minimum Range k-Cut Algorithm
Yang DaiKazuo IwanoNaoki Katoh
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1994 Volume 114 Issue 4 Pages 438-443

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Abstract

Given a connected undirected multigraph G=(V, E) with positive edge capacities and a positive integer k with k≥2, the minimum k-cut problem is to find a set S⊆E of minimum capacity whose removal leaves k connected components. It is known that this problem is NP-hard. In this paper we propose a new approximate algorithm for solving the minimum k-cut problem by using efficient algorithm for the minimum range k-cut problem. Our method is based on the association of the range value of a k-cut and its cut value when each edge weight is chosen uniformly randomly between 0 and 1. Though the closeness of our approximate solution has not yet been theoretically evaluated, we demonstrate its usefulness by performing computational experiments and comparing with another appoximate algorithm proposed by Saran and Vazirani. Our computational experiments show that the new method produces almost the same solutions or even better solutions for small k like k=3, 4, with running time much less than that for the algorithm of Saran and Vazirani.

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© The Institute of Electrical Engineers of Japan
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