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DOI: 10.4230/LIPIcs.SoCG.2020.15

The Reeb Graph Edit Distance Is Universal

Authors: Ulrich Bauer, Claudia Landi, and Facundo Mémoli

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

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.

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Ulrich Bauer, Claudia Landi, and Facundo Mémoli. The Reeb Graph Edit Distance Is Universal. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bauer_et_al:LIPIcs.SoCG.2020.15,
  author =	{Bauer, Ulrich and Landi, Claudia and M\'{e}moli, Facundo},
  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 =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.15},
  URN =		{urn:nbn:de:0030-drops-121730},
  doi =		{10.4230/LIPIcs.SoCG.2020.15},
  annote =	{Keywords: Reeb graphs, topological descriptors, edit distance, interleaving distance}
}

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The Reeb Graph Edit Distance Is Universal

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