Abstract
In topological data analysis, the matching distance is a computationally tractable metric on multifiltered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision ε > 0. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.
Original language | English |
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Title of host publication | 36th International Symposium on Computational Geometry, SoCG 2020 |
Editors | Sergio Cabello, Danny Z. Chen |
Place of Publication | Wadern |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Number of pages | 16 |
ISBN (Electronic) | 9783959771436 |
DOIs | |
Publication status | Published - 2020 |
Event | 36th International Symposium on Computational Geometry: SoCG 2020 - Zürich, Virtuell, Switzerland Duration: 23 Jun 2020 → 26 Jun 2020 https://socg20.inf.ethz.ch/socg |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 164 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 36th International Symposium on Computational Geometry |
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Abbreviated title | SoCG 2020 |
Country/Territory | Switzerland |
City | Virtuell |
Period | 23/06/20 → 26/06/20 |
Internet address |
Keywords
- Approximation algorithm
- Matching distance
- Multi-parameter persistence
ASJC Scopus subject areas
- Software