This article is cited in 7 papers

Mathematics

Estimates of Steiner subratio and Steiner–Gromov ratio

A. C. Pahkomova<sup>ab

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Delone Laboratory of Discrete and Computational Mathematics

Abstract: A lower bound for $n$-pointed Steiner subratio and Steiner–Gromov ratio was obtained. As a corollary of the main theorem, the value of these ratios was calculated for several metric spaces, for example, for philogenetic ones. It was also proved, that any number from 0,5 to 1 could be a Steiner subratio or a Steiner–Gromov ratio of a certain metric space.

Key words: Steiner subratio, Steiner–Gromov ratio, Steiner problem, minimal filling, shortest trees, minimal spanning trees, philogenetic spaces.

UDC: 519.176

Received: 02.04.2012

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2014, 69:1, 16–23

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