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This article is cited in 4 scientific papers (total in 4 papers)
The Gromov–Hausdorff distances to simplexes
D. S. Grigor'eva, A. O. Ivanovab, A. A. Tuzhilina a Faculty of Mechanics and Mathematics, Lomonosov Moscow State
University (Moscow)
b Bauman Moscow State Technical University (Moscow)
Abstract:
In the paper geometrical characteristics of metric spaces appearing in explicit formulas for the Gromov–Hausdorff distance from this spaces to so-called simplexes, i.e., the metric spaces, all whose non-zero distances are the same. For the calculation of those distances the geometry of partitions of these spaces is important. In the case of finite metric spaces that leads to some analogues of the edges lengths of minimal spanning trees. Earlier, a similar theory was elaborated for compact metric spaces. These results are generalised to the case of an arbitrary bounded metric space, explicit formulas are obtained, and some proofs are simplified.
Keywords:
Gromov–Hausdorff distance, metric geometry, metric space.
Received: 13.06.2019 Accepted: 12.07.2019
Citation:
D. S. Grigor'ev, A. O. Ivanov, A. A. Tuzhilin, “The Gromov–Hausdorff distances to simplexes”, Chebyshevskii Sb., 20:2 (2019), 108–122
Linking options:
https://www.mathnet.ru/eng/cheb756 https://www.mathnet.ru/eng/cheb/v20/i2/p108
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Abstract page: | 190 | Full-text PDF : | 70 | References: | 10 |
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