Tight quasi-universality of Reeb graph distances
Geometric Topology
2023-09-14 v4 Computational Geometry
Abstract
We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees we also prove strict universality of this distance. Furthermore, we prove that for the special case of merge trees the functional contortion distance coincides with the interleaving distance, yielding universality of all four distances in this case.
Keywords
Cite
@article{arxiv.2112.00720,
title = {Tight quasi-universality of Reeb graph distances},
author = {Ulrich Bauer and Håvard Bakke Bjerkevik and Benedikt Fluhr},
journal= {arXiv preprint arXiv:2112.00720},
year = {2023}
}
Comments
28 pages, 8 figures. This version establishes the tightness of all the bounds shown in the conference paper for SoCG 2022