  In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in
metric spaces, a generalization of the well-known Steiner tree problem.
Cost-distance Steiner trees minimize the sum of the total length and the
weighted path lengths from a dedicated root to the other terminals, which have
a weight to penalize the path length. They are applied when the tree is
intended for signal transmission, e.g. in chip design or telecommunication
networks, and the signal speed through the tree has to be considered besides
the total length. Constant factor approximation algorithms for the uniform
cost-distance Steiner tree problem have been known since the first mentioning
of the problem by Meyerson, Munagala, and Plotkin. Recently, the approximation
factor was improved from 2.87 to 2.39 by Khazraei and Held. We refine their
approach further and reduce the approximation factor down to 2.15.
