Algorithms for terminal Steiner trees

The terminal Steiner tree problem (TST) consists of finding a minimum cost Steiner tree where each terminal is a leaf. We describe a factor 2ρ−ρ/(3ρ−2) approximation algorithm for the TST, where ρ is the approximation factor of a given algorithm for the Steiner tree problem. Considering the current best value of ρ, this improves a previous 3.10 factor to 2.52. For the TST restricted to instances where all edge costs are either 1 or 2, we improve the approximation factor from 1.60 to 1.42.