Approximation algorithms for the 0-extension problem

In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semimetric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of the edge's weight and the distance between the terminals to which its endpoints are assigned. This problem generalizes the multiway cut problem of Dahlhaus, Johnson, Papadimitriou, Seymour, and Yannakakis and is closely related to the metric labeling problem introduced by Kleinberg and Tardos. We present approximation algorithms for 0-Extension. In arbitrary graphs, we present a O(log k)-approximation algorithm, k being the number of terminals. We also give O(1)approximation guarantees for weighted planar graphs. Our results are based on a natural metric relaxation of the problem, previously considered by Karzanov. It is similar in flavor to the linear programming relaxation of Garg, Vazirani, and Yannakakis for the multicut proble...

• Type: Conference
• Year: 2001
• Where: SODA
• Authors: Gruia Calinescu, Howard J. Karloff, Yuval Rabani
• Keywords: Algorithms, Linear Programming Relaxation, METRIC LABELING Problem, Metric Relaxations, SODA 2001