An analytical method for derivation of the Steiner Ratio of 3D euclidean Steiner trees

We stress the convenience of some analytical methods which have been introduced recently [Mondaini, R. P.: In: Nonconvex Optimization and its Applications series, pp. 373–390. Kluwer Acad. (2003); Mondaini, R. P.: In: BIOMAT 2005, International Symposium on Mathematical and Computational Biology, pp. 327–342. World Scientific Co Ltd (2006)] for calculating the Steiner Ratio of finite sets of points in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}^3$$\end{document} . These methods are good enough at reproducing the results obtained by reduction of the search space of numerical algorithms and can be easily extended to any number of dimensions.