The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces

Abstract

In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex's cardinality does not exceed the cardinality of $X$, a new formula for this distance is obtained. The latter permits to derive an exact formula for the distance between a simplex and an ultrametric space.

arXiv comment10 pages

References in corpus (4)

• Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes
• Gromov--Hausdorff Distance, Irreducible Correspondences, Steiner Problem, and Minimal Fillings
• Calculation of Minimum Spanning Tree Edges Lengths using Gromov--Hausdorff Distance
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Cited by in corpus (1)

• The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces