Metric Graph Approximations of Geodesic Spaces
Facundo Mémoli, Osman Berat Okutan, Wang, Qingsong · arXiv (Cornell University) · 2018
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.