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.

The Reeb Graph Edit Distance Is Universal / Bauer, ULRICH ALEXANDER; Landi, Claudia; Mémoli, Facundo. - 164:(2020), pp. 15:1-15:16. ((Intervento presentato al convegno 36th International Symposium on Computational Geometry (SoCG 2020) tenutosi a online (Zurich, CH) nel June 22-26, 2020 [10.4230/lipics.socg.2020.15].

The Reeb Graph Edit Distance Is Universal

Ulrich Bauer;Claudia Landi;
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.
36th International Symposium on Computational Geometry (SoCG 2020)
online (Zurich, CH)
June 22-26, 2020
164
15:1
15:16
Bauer, ULRICH ALEXANDER; Landi, Claudia; Mémoli, Facundo
The Reeb Graph Edit Distance Is Universal / Bauer, ULRICH ALEXANDER; Landi, Claudia; Mémoli, Facundo. - 164:(2020), pp. 15:1-15:16. ((Intervento presentato al convegno 36th International Symposium on Computational Geometry (SoCG 2020) tenutosi a online (Zurich, CH) nel June 22-26, 2020 [10.4230/lipics.socg.2020.15].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1203672
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