2026-07-26T00:39:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16022 2024-03-06T10:56:45Z ddc:004 open_access

Quasi-Universality of Reeb Graph Distances Bauer, Ulrich Bjerkevik, Håvard Bakke Fluhr, Benedikt Reeb graphs contour trees merge trees distances universality interleaving distance functional distortion distance functional contortion distance We establish 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ulrich Bauer and Håvard Bakke Bjerkevik and Benedikt Fluhr 2022 Is Part Of LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2022.14 urn:nbn:de:0030-drops-160221 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.14 eng https://creativecommons.org/licenses/by/4.0/legalcode