Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Michael Kerber, Arnur Nigmetov

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem Konferenzband

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.

Originalspracheenglisch
Titel36th International Symposium on Computational Geometry, SoCG 2020
Redakteure/-innenSergio Cabello, Danny Z. Chen
ErscheinungsortWadern
Herausgeber (Verlag)Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
Seitenumfang16
ISBN (elektronisch)9783959771436
DOIs
PublikationsstatusVeröffentlicht - 2020
Veranstaltung36th International Symposium on Computational Geometry - Virtuell, Schweiz
Dauer: 23 Jun 202026 Jun 2020

Publikationsreihe

NameLeibniz International Proceedings in Informatics, LIPIcs
Band164
ISSN (Print)1868-8969

Konferenz

Konferenz36th International Symposium on Computational Geometry
KurztitelSoCG 2020
LandSchweiz
OrtVirtuell
Zeitraum23/06/2026/06/20

ASJC Scopus subject areas

  • Software

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