@inproceedings{a96efef5be19410f9eb9fd2699a3183d,
title = "The Reeb graph edit distance is universal",
abstract = "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.",
keywords = "Edit distance, Interleaving distance, Reeb graphs, Topological descriptors",
author = "Ulrich Bauer and Claudia Landi and Facundo M{\'e}moli",
note = "Publisher Copyright: {\textcopyright} Ulrich Bauer, Claudia Landi, and Facundo M{\'e}moli; licensed under Creative Commons License CC-BY 36th International Symposium on Computational Geometry (SoCG 2020).; 36th International Symposium on Computational Geometry, SoCG 2020 ; Conference date: 23-06-2020 Through 26-06-2020",
year = "2020",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2020.15",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Sergio Cabello and Chen, {Danny Z.}",
booktitle = "36th International Symposium on Computational Geometry, SoCG 2020",
}