Optimal 3-terminal cuts and linear programming

Given an undirected graph G = (V;E) and three speci ed 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 GnA. If a non-negative edge weight ce is speci ed for each e 2 E, the optimal 3-cut problem is to nd 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 Calinescu, Karlo , 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

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Kevin K. H. Cheung, William H. Cunningham, Lawrence Tang
• Keywords: Approximation Algorithm, MP 2006, Non-negative Edge Weight, Optimal 3-cut Problem