Mathematical Programming

, Volume 150, Issue 1, pp 19–34 | Cite as

A 3/2-approximation algorithm for some minimum-cost graph problems

  • Basile Couëtoux
  • James M. Davis
  • David P. WilliamsonEmail author
Full Length Paper Series B


We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter \(k\), and want to find a forest such that each component has at least \(k\) vertices. Goemans and Williamson gave a 2-approximation algorithm for this class of problems. We give an improved 3/2-approximation algorithm.

Mathematics Subject Classification

90C27 05C85 



We thank anonymous reviewers of this paper for useful comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013

Authors and Affiliations

  • Basile Couëtoux
    • 1
  • James M. Davis
    • 2
  • David P. Williamson
    • 2
    Email author
  1. 1.Laboratoire d’Informatique Fondamentale de MarseilleUniversité de la MediterranéeMarseille Cedex 9France
  2. 2.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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