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; Landi, Claudia; Mémoli, Facundo. - In: FOUNDATIONS OF COMPUTATIONAL MATHEMATICS. - ISSN 1615-3375. - 21:(2020), pp. 1441-1464. [10.1007/s10208-020-09488-3]
The Reeb Graph Edit Distance is Universal
Bauer, Ulrich;Landi, Claudia;
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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