18 citations · 133 across the 33 of their papers we have counts for
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Who Invented the Gromov-Hausdorff Distance?
Alexey A. Tuzhilin
One of the most beautiful notions of metric geometry is the Gromov-Hausdorff distance which measures the difference between two metric spaces. To define the distance, let us isomet…
Local Structure of Gromov-Hausdorff Space near Finite Metric Spaces in General Position
Alexander O. Ivanov, Alexey A. Tuzhilin
We investigate the local structure of the space consisting of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We consider finite…
Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes
Alexander O. Ivanov, Alexey A. Tuzhilin
In the present paper we investigate geometric characteristics of compact metric spaces, which can be described in terms of Gromov-Hausdorff distances to simplexes, i.e., to finite…
Calculation of Minimum Spanning Tree Edges Lengths using Gromov--Hausdorff Distance
Alexey A. Tuzhilin
In the present paper we show how one can calculate the lengths of edges of a minimum spanning tree constructed for a finite metric space, in terms of the Gromov-Hausdorff distances…
Steiner Ratio and Steiner-Gromov Ratio of Gromov-Hausdorff Space
Alexander Ivanov, Alexey Tuzhilin
In the present paper we investigate the metric space consisting of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We show that for an…
Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of Finite Metric Spaces into this Space
Stavros Iliadis, Alexander Ivanov, Alexey Tuzhilin
We investigate the geometry of the family of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We show that sufficiently small neighborh…