Abstract
Given an undirected graph G=(V,E) and three specified terminal nodes t1,t2,t3, a 3-cut is a subset A of E such that no two terminals are in the same component of G\A. If a non-negative edge weight ce is specified for each e∈E, the optimal 3-cut problem is to find a 3-cut of minimum total weight. This problem is **-hard, and in fact, is max-** -hard. An approximation algorithm having performance guarantee ** has recently been given by Călinescu, Karloff, and Rabani. It is based on a certain linear-programming relaxation, for which it is shown that the optimal 3-cut has weight at most ** times the optimal LP value. It is proved here that ** can be improved to **, and that this is best possible. As a consequence, we obtain an approximation algorithm for the optimal 3-cut problem having performance guarantee **. In addition, we show that ** is best possible for this algorithm.
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