**thm 3.2 in text:*** there is an approximation-preserving reduction from the minimum-cost Steiner tree problem in general graphs to the minimum-cost Steiner tree problem in metric graphs.*

**corollary:*** there exists a 2-approximation algorithm for the minimum-cost Steiner tree problem.*

references:

- Chapter 3 of Approximation Algorithms by Vijay Vazirani.