License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2020.15
URN: urn:nbn:de:0030-drops-121730
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12173/
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Bauer, Ulrich ; Landi, Claudia ; Mémoli, Facundo

The Reeb Graph Edit Distance Is Universal

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LIPIcs-SoCG-2020-15.pdf (0.5 MB)


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.

BibTeX - Entry

@InProceedings{bauer_et_al:LIPIcs:2020:12173,
  author =	{Ulrich Bauer and Claudia Landi and Facundo M{\'e}moli},
  title =	{{The Reeb Graph Edit Distance Is Universal}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12173},
  URN =		{urn:nbn:de:0030-drops-121730},
  doi =		{10.4230/LIPIcs.SoCG.2020.15},
  annote =	{Keywords: Reeb graphs, topological descriptors, edit distance, interleaving distance}
}

Keywords: Reeb graphs, topological descriptors, edit distance, interleaving distance
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020


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