Graphics and networks – Steiner approach tree.

I wonder about the existence of the Mathematica code to find (approximate) the Steiner trees in the graphics. I know there are a number of algorithms to do it, just out of curiosity if someone has implemented any of these in a Mathematica context.

The graphics that interest me have a maximum of 300 vertices. I would also like to know if someone has implemented (in Mathematica) an exact algorithm that runs for so many vertices in less than one life.