Name
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10208-020-09488-3 | FOUNDATIONS OF COMPUTATIONAL MATHEMATICS |
Keywords | Field | DocType |
Reeb graphs, Stability, Quotient metric, Edit distance | Edit distance,Discrete mathematics,Graph,Uniform norm,Algebra,Upper and lower bounds,Distortion,Piecewise linear function,Interleaving,Mathematics,Reeb graph | Journal |
Volume | Issue | ISSN |
21 | 5 | 1615-3375 |
Citations | PageRank | References |
1 | 0.37 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Claudia Landi | 2 | 161 | 16.18 |
| Facundo Mémoli | 3 | 735 | 43.44 |