Abstract
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.
| Original language | English |
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| Title of host publication | 38th International Symposium on Computational Geometry (SoCG 2022) |
| Editors | Xavier Goaoc, Michael Kerber |
| Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
| Pages | 14:1-14:18 |
| ISBN (Electronic) | 978-3-95977-227-3 |
| DOIs | |
| Publication status | Published - 1 Jun 2022 |
| Event | 38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Germany Duration: 7 Jun 2022 → 10 Jun 2022 https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 224 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 38th International Symposium on Computational Geometry |
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| Abbreviated title | SoCG 2022 |
| Country/Territory | Germany |
| City | Berlin |
| Period | 7/06/22 → 10/06/22 |
| Internet address |
Keywords
- contour trees
- distances
- functional contortion distance
- functional distortion distance
- interleaving distance
- merge trees
- Reeb graphs
- universality
ASJC Scopus subject areas
- Software
Fields of Expertise
- Information, Communication & Computing