2026-07-24T03:28:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23158 2025-10-02T12:41:27Z ddc:004 open_access

A Sparse Multicover Bifiltration of Linear Size Alonso, Ángel Javier Multicover Approximation Sparsification Multiparameter persistence The k-cover of a point cloud X of ℝ^d at radius r is the set of all those points within distance r of at least k points of X. By varying r and k we obtain a two-parameter filtration known as the multicover bifiltration. This bifiltration has received attention recently due to being choice-free and robust to outliers. However, it is hard to compute: the smallest known equivalent simplicial bifiltration has O(|X|^{d+1}) simplices. In this paper we introduce a (1+ε)-approximation of the multicover bifiltration of linear size O(|X|), for fixed d and ε. The methods also apply to the subdivision Rips bifiltration on metric spaces of bounded doubling dimension yielding analogous results. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ángel Javier Alonso 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.6 urn:nbn:de:0030-drops-231587 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.6 eng https://creativecommons.org/licenses/by/4.0/legalcode