2026-07-23T07:02:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12211 2024-03-06T10:49:43Z ddc:004 open_access

Efficient Approximation of the Matching Distance for 2-Parameter Persistence Kerber, Michael Nigmetov, Arnur multi-parameter persistence matching distance approximation algorithm In topological data analysis, the matching distance is a computationally tractable metric on multi-filtered 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michael Kerber and Arnur Nigmetov 2020 Is Part Of LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2020.53 urn:nbn:de:0030-drops-122116 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.53 eng https://creativecommons.org/licenses/by/3.0/legalcode