An Analytical Method for Derivation of the Steiner Ratio of 3D Euclidean Steiner Trees

摘要

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 R~3. 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.