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The Reeb Graph Edit Distance Is Universal

Authors Ulrich Bauer , Claudia Landi , Facundo Mémoli

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Algebraic topology
Keywords
  • Reeb graphs
  • topological descriptors
  • edit distance
  • interleaving distance

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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.

Cite As Get BibTex

Ulrich Bauer, Claudia Landi, and Facundo Mémoli. The Reeb Graph Edit Distance Is Universal. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SoCG.2020.15

Author Details

Ulrich Bauer
  • Department of Mathematics, Technical University of Munich (TUM), Germany
Claudia Landi
  • Dipartimento di Scienze e Metodi dell'Ingegneria, Università degli Studi di Modena e Reggio Emilia, Reggio Emilia, Italy
Facundo Mémoli
  • Department of Mathematics, The Ohio State University, Columbus, OH, USA

Funding

This research has been partially supported by FAR 2014 (UniMORE), ARCES (University of Bologna), and the DFG Collaborative Research Center SFB/TRR 109 "Discretization in Geometry and Dynamics".

Acknowledgements

We thank Barbara Di Fabio and Yusu Wang for valuable discussions.

References

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