Isometry Group of Gromov--Hausdorff Space
A Ivanov, A Tuzhilin - arXiv preprint arXiv:1806.02100, 2018 - arxiv.org
The present paper is devoted to investigation of the isometry group of the Gromov-Hausdorff
space, ie, the metric space of compact metric spaces considered up to an isometry and …
space, ie, the metric space of compact metric spaces considered up to an isometry and …
Local structure of Gromov–Hausdorff space around generic finite metric spaces
AO Ivanov, AA Tuzhilin - Lobachevskii Journal of Mathematics, 2017 - Springer
We investigate the local structure of the space M consisting of isometry classes of compact
metric spaces, endowed with the Gromov–Hausdorff metric. We consider finite metric spaces …
metric spaces, endowed with the Gromov–Hausdorff metric. We consider finite metric spaces …
Gromov--Hausdorff Distance to Simplexes
DS Grigor'ev, AO Ivanov, AA Tuzhilin - arXiv preprint arXiv:1906.09644, 2019 - arxiv.org
Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff
distances from these spaces to so-called simplexes, ie, to the metric spaces, all whose non …
distances from these spaces to so-called simplexes, ie, to the metric spaces, all whose non …
Расстояния Громова-Хаусдорфа до симплексов
ДС Григорьев, АО Иванов, АА Тужилин - Чебышевский сборник, 2019 - cyberleninka.ru
В работе изучаются геометрические характеристики метрических пространств,
участвующие в формулах расстояний Громова-Хаусдорфа от этих пространств до так …
участвующие в формулах расстояний Громова-Хаусдорфа от этих пространств до так …
Gromov-Hausdorff distances to Simplexes and some applications to Discrete Optimisation
IA Olegovich, TA Augustinovich - Чебышевский сборник, 2020 - cyberleninka.ru
Relations between Gromov-Hausdorff distance and Discrete Optimisation problems are
discussed. We use the Gromov-Hausdorff distances to single-distance metric space for …
discussed. We use the Gromov-Hausdorff distances to single-distance metric space for …
The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces
AO Ivanov, AA Tuzhilin - arXiv preprint arXiv:1907.09942, 2019 - arxiv.org
In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary
simplex (a metric space all whose non-zero distances are the same) and a finite metric …
simplex (a metric space all whose non-zero distances are the same) and a finite metric …
The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces
AO Ivanov, AA Tuzhilin - arXiv preprint arXiv:1907.03828, 2019 - arxiv.org
In the present paper we investigate the Gromov--Hausdorff distances between a bounded
metric space $ X $ and so called simplex, ie, a metric space all whose non-zero distances …
metric space $ X $ and so called simplex, ie, a metric space all whose non-zero distances …
Lipschitz (non-) equivalence of the Gromov--Hausdorff distances, including on ultrametric spaces
The Gromov--Hausdorff distance measures the difference in shape between compact metric
spaces. While even approximating the distance up to any practical factor poses an NP-hard …
spaces. While even approximating the distance up to any practical factor poses an NP-hard …
Hausdorff mapping: 1-Lipschitz and isometry properties
IA Mikhailov - Moscow University Mathematics Bulletin, 2018 - Springer
Abstract Properties of the Hausdorff mapping H taking each compact metric space to the
space of its non-empty closed subsets endowed with the Hausdorff metric are studied. It is …
space of its non-empty closed subsets endowed with the Hausdorff metric are studied. It is …
Расстояния Громова—Хаусдорфа до симплексов и некоторые приложения к дискретной оптимизации
АО Иванов, АА Тужилин - Чебышевский сборник, 2020 - chebsbornik.ru
Аннотация В работе изучается взаимосвязь между расстоянием Громова—Хаусдорфа
и задачами дискретной оптимизации. Расстояние Громова—Хаусдорфа до …
и задачами дискретной оптимизации. Расстояние Громова—Хаусдорфа до …