SteinerTree

thm 3.3 in text: in a metric graph, the cost of the MST of a set of vertices S is at most twice the cost of the minimum-cost Steiner tree for S

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.

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references:

• Chapter 3 of Approximation Algorithms by Vijay Vazirani.