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, defined as the maximum possible degree of a minimum-degree MST spanning points from the space. In particular, on instances drawn from the Euclidean (resp. rectilinear) plane, the MST heuristic is shown to have tight approximation factors of 4, respectively 3. Keywords: Approximation algorithms, Steiner trees, MST heuristic, fixed wireless network design, VLSI CAD. 1 Introduction The classical Steiner tree problem is that of finding a shortest tree spanning a given set of terminal points. The tree may use additional points besides the terminals, these points are commonly referred to as Steiner points. In the Minimum number of Steiner Points Tree (MSPT) problem [7,5] one also seeks a tree ..
