4 citations · 13 across the 13 of their papers we have counts for
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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…
Gromov--Hausdorff Distance, Irreducible Correspondences, Steiner Problem, and Minimal Fillings
Alexander Ivanov, Alexey Tuzhilin
We introduce irreducible correspondences that enables us to calculate the Gromov--Hausdorff distances effectively. By means of these correspondences, we show that the set of all me…
Steiner Problem in Gromov-Hausdorff Space: the Case of Finite Metric Spaces
Alexander Ivanov, Nadezhda Nikolaeva, Alexey Tuzhilin
It is shown that each finite family of finite metric spaces, being considered as a subset of Gromov--Hausdorff space, can be connected by a Steiner minimal tree.
Realizations of Gromov-Hausdorff Distance
Alexander Ivanov, Stavros Iliadis, Alexey Tuzhilin
It is shown that for any two compact metric spaces there exists an "optimal" correspondence which the Gromov-Hausdorff distance is attained at. Each such correspondence generates i…