I keep encountering citations of the following article:
Takahashi and A. Matsuyama, “An approximate solution for the Steiner problem in graphs,” Math. Japonica, vol. 24, no. 6, pp. 573–577, 1980
For example, Yahui Sun refers to it here as "a widely-used Steiner tree approximation algorithm".
But... what is the actual algorithm?
The website of Mathematica Japonica only goes back to 1994, and I can't find the article anywhere else either.
Wikipedia contains this description, but without a citation:
The general graph Steiner tree problem can be approximated by computing the minimum spanning tree of the subgraph of the metric closure of the graph induced by the terminal vertices. The metric closure of a graph G is the complete graph in which each edge is weighted by the shortest path distance between the nodes in G. This algorithm produces a tree whose weight is within a 2 − 2/t factor of the weight of the optimal Steiner tree where t is the number of leaves in the optimal Steiner tree; this can be proven by considering a traveling salesperson tour on the optimal Steiner tree. The approximate solution is computable in polynomial time by first solving the all-pairs shortest paths problem to compute the metric closure, then by solving the minimum spanning tree problem.
Is this the algorithm that Sun and others refer to?