Mathematical Programming

, Volume 100, Issue 2, pp 411–421 | Cite as

Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation

  • Fabián A. Chudak
  • Tim Roughgarden
  • David P. WilliamsonEmail author


Garg [10] gives two approximation algorithms for the minimum-cost tree spanning k vertices in an undirected graph. Recently Jain and Vazirani [15] 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.


Approximation Algorithm Constant Factor Undirected Graph Facility Location Similar Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fabián A. Chudak
    • 1
  • Tim Roughgarden
    • 2
  • David P. Williamson
    • 3
    Email author
  1. 1.ETH ZurichInstitut für Operations ResearchZürichSwitzerland
  2. 2.University of California at BerkeleyComputer Science DepartmentBerkeleyUSA
  3. 3.IBM Almaden Research CenterSan JoseUSA

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