2026-09-05T12:01:35Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25811 2026-06-24T14:54:21Z ddc:004 open_access

Bifunction and Interlevel Delaunay Trifiltrations Alonso, Ángel Javier Kerber, Michael Lam, Tung Lesnick, Michael Rathod, Abhishek Delaunay triangulation Multiparameter persistent homology Interlevel Bowyer-Watson A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extended to point clouds equipped with an ℝ-valued function, yielding a computable 2-parameter filtration that satisfies an analogous weak equivalence. Motivated in part by the study of time-varying data, we introduce a 3-parameter extension of the Delaunay filtration for point clouds equipped with an ℝ²-valued function, also satisfying an analogous weak equivalence. For a point cloud X ⊂ ℝ^d, our trifiltration has size O(|X|^{⌈(d+1)/2⌉+1}). We present an algorithm that computes this trifiltration in time O(|X|^{⌈d/2⌉+2}), together with an implementation. Our experiments demonstrate that the implementation can handle thousands of points in ℝ³, with memory growth that is nearly linear. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ángel Javier Alonso and Michael Kerber and Tung Lam and Michael Lesnick and Abhishek Rathod 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.5 urn:nbn:de:0030-drops-258118 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.5 eng https://creativecommons.org/licenses/by/4.0/legalcode