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Uniform cost-distance Steiner trees minimize the sum of the total length andweighted path lengths from a dedicated root to the other terminals. They areapplied when the tree is intended for signal transmission, e.g. in chip designor telecommunication networks. They are a special case of general cost-distanceSteiner trees, where different distance functions are used for total length andpath lengths.  We improve the best published approximation factor for the uniformcost-distance Steiner tree problem from 2.39 to 2.05. If we can approximate theminimum-length Steiner tree problem arbitrarily well, our algorithm achieves anapproximation factor arbitrarily close to $ 1 + \frac{1}{\sqrt{2}} $. Thisbound is tight in the following sense. We also prove the gap $ 1 +\frac{1}{\sqrt{2}} $ between optimum solutions and the lower bound which we andall previous approximation algorithms for this problem use.  Similarly to previous approaches, we start with an approximate minimum-lengthSteiner tree and split it into subtrees that are later re-connected. To improvethe approximation factor, we split it into components more carefully, takingthe cost structure into account, and we significantly enhance the analysis.

Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem