Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation

Garg [10] gives two approximation algorithms for the minimum-cost tree spanning k vertices in an undirected graph. Recently Jain and Vazirani [16] discovered primal-dual approximation algorithms for the metric uncapacitated facility location and k-median problems. In this paper we show how Garg's algorithms can be explained simply with ideas introduced by Jain and Vazirani, in particular via a Lagrangean relaxation technique together with the primal-dual method for approximation algorithms. We also derive a constant factor approximation algorithm for the k-Steiner tree problem using these ideas, and point out the common features of these problems that allow them to be solved with similar techniques.

• Type: Conference
• Year: 2001
• Where: IPCO
• Authors: Fabián A. Chudak, Tim Roughgarden, David P. Williamson
• Keywords: Approximation Algorithm, Constant Factor Approximation Algorithm, IPCO 2001, IPCO 2007, Primal-dual Approximation Algorithms