The Reeb Graph Edit Distance is Universal

Ulrich Bauer, Claudia Landi, Facundo Mémoli

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Pages (from-to)1441-1464
Number of pages24
JournalFoundations of Computational Mathematics
Volume21
Issue number5
DOIs
StatePublished - Oct 2021

Keywords

  • Edit distance
  • Quotient metric
  • Reeb graphs
  • Stability

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