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

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## Abstract

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## Notes

### Acknowledgments

We thank anonymous reviewers of this paper for useful comments.

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