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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.15
URN: urn:nbn:de:0030-drops-178656
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17865/
Bauer, Ulrich ;
Lenzen, Fabian ;
Lesnick, Michael
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.
BibTeX - Entry
@InProceedings{bauer_et_al:LIPIcs.SoCG.2023.15,
author = {Bauer, Ulrich and Lenzen, Fabian and Lesnick, Michael},
title = {{Efficient Two-Parameter Persistence Computation via Cohomology}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {15:1--15:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-273-0},
ISSN = {1868-8969},
year = {2023},
volume = {258},
editor = {Chambers, Erin W. and Gudmundsson, Joachim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17865},
URN = {urn:nbn:de:0030-drops-178656},
doi = {10.4230/LIPIcs.SoCG.2023.15},
annote = {Keywords: Persistent homology, persistent cohomology, two-parameter persistence, clearing}
}
