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math.MG2019★ 2 cited
The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces
Alexander O. Ivanov, Alexey A. Tuzhilin
In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space and so called simplex, i.e., a metric space all whose non-zero distances are…
math.MG2019★ 4 cited
Gromov--Hausdorff Distance to Simplexes
D. S. Grigor'ev, A. O. Ivanov, A. A. Tuzhilin
Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whos…
math.MG2019★ 2 cited
Hausdorff Realization of Linear Geodesics of Gromov-Hausdorff Space
Alexander O. Ivanov, Alexey A. Tuzhilin
We have constructed a realization of rectilinear geodesic (in the sense of~\cite{Memoli2018}), lying in Gromov-Hausdorff space, as a shortest geodesic w.r.t. the Hausdorff distance…