A polylogarithmic approximation for computing non-metric terminal Steiner trees

The main contribution of this short note is to provide improved bounds on the approximability of constructing terminal Steiner trees in arbitrary undirected graphs. Technically speaking, our results are obtained by relating this computational task to that of computing group Steiner trees. As a secondary objective, we make a concentrated effort to distinguish between the factor by which constructed trees exceed the optimal backbone cost and between the deviation from the optimal terminal linking cost.