Metric Graph Approximations of Geodesic Spaces
Metric Geometry
2023-10-27 v5
Abstract
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitable multiplicative constant, Reeb graphs of distance functions to a point provide optimal approximation in the Gromov-Hausdsorff sense.
Cite
@article{arxiv.1809.05566,
title = {Metric Graph Approximations of Geodesic Spaces},
author = {Facundo Memoli and Osman Berat Okutan and Qingsong Wang},
journal= {arXiv preprint arXiv:1809.05566},
year = {2023}
}
Comments
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