Paper Info
Title
Approximation algorithms for the 0-extension problem
Abstract
In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semi-metric 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 O-EXTENSION. In arbitrary graphs, we present an &Ogr;(log k)-approximation algorithm, k being the number of terminals. We also give &Ogr;(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 problem and similar to relaxations for other graph partitioning problems. We prove that the integrality ratio of the metric relaxation is at least c√lgk for a positive c for infinitely many k. Our results improve some of the results of Kleinberg and Tardos and they further our understanding on how to use metric relaxations.
Year
DOI
Venue
2004
10.1145/365411.365413
SIAM J. Comput.
Keywords
Field
DocType
graph partitioning,approximation algorithm,metric space,linear programming relaxation
Discrete mathematics,Approximation algorithm,Graph,Combinatorics,Metric k-center,Graph partition,Linear programming relaxation,Planar graph,Mathematics,Labeling Problem
Journal
Volume
Issue
ISSN
34
2
0097-5397
ISBN
Citations 
PageRank 
0-89871-490-7
58
4.51
References 
Authors
18
3
Name
Order
Citations
PageRank
Gruia Calinescu1148794.99
Howard Karloff21673195.13
Yuval Rabani32265274.98