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

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Abstract

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 \({\mathbb{R}}^3\) . 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.

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  1. Federal University of Rio de Janeiro, UFRJ – COPPE – Centre of Technology, P.O. Box 68511, 21941-972, Rio de Janeiro, RJ, Brazil

    R. P. Mondaini

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  1. R. P. Mondaini
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Correspondence to R. P. Mondaini.

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Mondaini, R.P. An analytical method for derivation of the Steiner Ratio of 3D euclidean Steiner trees. J Glob Optim 43, 459–470 (2009). https://doi.org/10.1007/s10898-007-9163-z

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