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.
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