A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points

We give a tight analysis of the MST heuristic recently introduced by G.-H. Lin and G. Xue for approximating the Steiner tree with minimum number of Steiner points and bounded edge-lengths. The approximation factor of the heuristic is shown to be one less than the MST number of the underlying space, de ned as the maximum possible degree of a minimum-degree MST spanning points from the space. In particular, on instances drawn from the rectilinear (resp. Euclidean) plane, the MST heuristic is shown to have tight approximation factors of 3, respectively 4.