@inproceedings{1aab19a8ca8842df86bd2c57e46ecf8d,
title = "Efficient Two-Parameter Persistence Computation via Cohomology",
abstract = "Clearing is a simple but effective optimization for the standard algorithm of persistent homology (ph), which dramatically improves the speed and scalability of ph computations for Vietoris-Rips filtrations. Due to the quick growth of the boundary matrices of a Vietoris-Rips filtration with increasing dimension, clearing is only effective when used in conjunction with a dual (cohomological) variant of the standard algorithm. This approach has not previously been applied successfully to the computation of two-parameter ph. We introduce a cohomological algorithm for computing minimal free resolutions of two-parameter ph that allows for clearing. To derive our algorithm, we extend the duality principles which underlie the one-parameter approach to the two-parameter setting. We provide an implementation and report experimental run times for function-Rips filtrations. Our method is faster than the current state-of-the-art by a factor of up to 20.",
keywords = "Persistent homology, clearing, persistent cohomology, two-parameter persistence",
author = "Ulrich Bauer and Fabian Lenzen and Michael Lesnick",
note = "Publisher Copyright: {\textcopyright} Ulrich Bauer, Fabian Lenzen, and Michael Lesnick; licensed under Creative Commons License CC-BY 4.0.; 39th International Symposium on Computational Geometry, SoCG 2023 ; Conference date: 12-06-2023 Through 15-06-2023",
year = "2023",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2023.15",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Chambers, {Erin W.} and Gudmundsson, {Joachim }",
booktitle = "39th International Symposium on Computational Geometry, SoCG 2023",
}