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Steiner Ratio and Steiner-Gromov Ratio of Gromov-Hausdorff Spaceстатья
- Авторы: Alexandr Ivanov, Alexey Tuzhilin
- Журнал: ArXiv e-prints
- Номер: 1605.01094
- Год издания: 2016
- Аннотация: In the present paper we investigate the metric space $\cM$ consisting of isometry classes of compact metric spaces, endowed with the Gromov--Hausdorff metric. We show that for any finite subset $M$ from a sufficiently small neighborhood of a generic finite metric space, providing $M$ consists of finite metric spaces with the same number of points, each Steiner minimal tree in $\cM$ connecting $M$ is a minimal filling for $M$. As a consequence, we prove that the both Steiner ratio and Gromov--Steiner ratio of $\cM$ are equal to $1/2$.
- Добавил в систему: Тужилин Алексей Августинович