2026-07-26T08:01:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12173 2024-03-06T10:49:37Z ddc:004 open_access

The Reeb Graph Edit Distance Is Universal Bauer, Ulrich Landi, Claudia Mémoli, Facundo Reeb graphs topological descriptors edit distance interleaving distance We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ulrich Bauer and Claudia Landi and Facundo Mémoli 2020 Is Part Of LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2020.15 urn:nbn:de:0030-drops-121730 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.15 eng https://creativecommons.org/licenses/by/3.0/legalcode