Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Michael Kerber, Arnur Nigmetov

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

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 languageEnglish
Title of host publication36th International Symposium on Computational Geometry, SoCG 2020
EditorsSergio Cabello, Danny Z. Chen
Place of PublicationWadern
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
Number of pages16
ISBN (Electronic)9783959771436
DOIs
Publication statusPublished - 2020
Event36th International Symposium on Computational Geometry: SoCG 2020 - Zürich, Virtuell, Switzerland
Duration: 23 Jun 202026 Jun 2020
https://socg20.inf.ethz.ch/socg

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume164
ISSN (Print)1868-8969

Conference

Conference36th International Symposium on Computational Geometry
Abbreviated titleSoCG 2020
CountrySwitzerland
CityVirtuell
Period23/06/2026/06/20
Internet address

Keywords

  • Approximation algorithm
  • Matching distance
  • Multi-parameter persistence

ASJC Scopus subject areas

  • Software

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