Abstract
Given an undirected graph G = (V,E) and three specified terminal nodes t 1,t 2,t 3, 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 c e is specified for each e ∈ E, the optimal 3-cut problem is to find a 3-cut of minimum total weight. This problem is NP-hard, and in fact, is max-SNP-hard. An approximation algorithm having performance guarantee 7/6 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 7/6 times the optimal LP value. It is proved here that 7/6 can be improved to 12/11, and that this is best possible. As a consequence, we obtain an approximation algorithm for the optimal 3-cut problem having performance guarantee 12/11.
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© 1999 Springer-Verlag Berlin Heidelberg
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Cunningham, W.H., Tang, L. (1999). Optimal 3-Terminal Cuts and Linear Programming. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_9
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DOI: https://doi.org/10.1007/3-540-48777-8_9
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