---
_id: '2044'
abstract:
- lang: eng
text: We present a parallel algorithm for computing the persistent homology of a
filtered chain complex. Our approach differs from the commonly used reduction
algorithm by first computing persistence pairs within local chunks, then simplifying
the unpaired columns, and finally applying standard reduction on the simplified
matrix. The approach generalizes a technique by Günther et al., which uses discrete
Morse Theory to compute persistence; we derive the same worst-case complexity
bound in a more general context. The algorithm employs several practical optimization
techniques, which are of independent interest. Our sequential implementation of
the algorithm is competitive with state-of-the-art methods, and we further improve
the performance through parallel computation.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent
Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III. Mathematics and Visualization.
Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing
Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R.
Peikert (Eds.), Topological Methods in Data Analysis and Visualization III
(pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7'
chicago: 'Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress:
Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis
and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.'
ieee: 'U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent
Homology in Chunks,” in Topological Methods in Data Analysis and Visualization
III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014,
pp. 103–117.'
ista: 'Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent
Homology in Chunks. In: Topological Methods in Data Analysis and Visualization
III. , 103–117.'
mla: 'Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in
Chunks.” Topological Methods in Data Analysis and Visualization III, edited
by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.'
short: U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci,
R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III,
Springer, 2014, pp. 103–117.
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_7
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1303.0477
month: '03'
oa: 1
oa_version: Submitted Version
page: 103 - 117
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III
publication_status: published
publisher: Springer
publist_id: '5007'
quality_controlled: '1'
scopus_import: 1
series_title: Mathematics and Visualization
status: public
title: 'Clear and Compress: Computing Persistent Homology in Chunks'
type: book_chapter
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...