---
_id: '1842'
abstract:
- lang: eng
text: We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2
outerplanar triangulations in both convex and general cases. We also prove that
the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by
O(n3) and O(n10), in the convex and general case, respectively. We then apply
similar methods to prove an (Formula presented.) upper bound on the Ramsey number
of a path with n ordered vertices.
acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165.
article_processing_charge: No
arxiv: 1
author:
- first_name: Josef
full_name: Cibulka, Josef
last_name: Cibulka
- first_name: Pu
full_name: Gao, Pu
last_name: Gao
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Tomáš
full_name: Valla, Tomáš
last_name: Valla
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
citation:
ama: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number
of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79.
doi:10.1007/s00454-014-9646-x
apa: Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the
geometric ramsey number of outerplanar graphs. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x
chicago: Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On
the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational
Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.
ieee: J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey
number of outerplanar graphs,” Discrete & Computational Geometry, vol.
53, no. 1. Springer, pp. 64–79, 2014.
ista: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey
number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.
mla: Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.”
Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014,
pp. 64–79, doi:10.1007/s00454-014-9646-x.
short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational
Geometry 53 (2014) 64–79.
date_created: 2018-12-11T11:54:18Z
date_published: 2014-11-14T00:00:00Z
date_updated: 2025-09-29T13:11:56Z
day: '14'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-014-9646-x
external_id:
arxiv:
- '1310.7004'
isi:
- '000346774600005'
intvolume: ' 53'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.7004
month: '11'
oa: 1
oa_version: Submitted Version
page: 64 - 79
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5260'
scopus_import: '1'
status: public
title: On the geometric ramsey number of outerplanar graphs
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 53
year: '2014'
...
---
OA_place: repository
OA_type: green
_id: '2012'
abstract:
- lang: eng
text: The classical sphere packing problem asks for the best (infinite) arrangement
of non-overlapping unit balls which cover as much space as possible. We define
a generalized version of the problem, where we allow each ball a limited amount
of overlap with other balls. We study two natural choices of overlap measures
and obtain the optimal lattice packings in a parameterized family of lattices
which contains the FCC, BCC, and integer lattice.
acknowledgement: We thank Herbert Edelsbrunner for his valuable discussions and ideas
on the topic of this paper. The second author has been supported by the Max Planck
Center for Visual Computing and Communication
article_processing_charge: No
arxiv: 1
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: 'Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. In:
26th Canadian Conference on Computational Geometry. Canadian Conference
on Computational Geometry; 2014:155-161.'
apa: 'Iglesias Ham, M., Kerber, M., & Uhler, C. (2014). Sphere packing with
limited overlap. In 26th Canadian Conference on Computational Geometry
(pp. 155–161). Halifax, Canada: Canadian Conference on Computational Geometry.'
chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing
with Limited Overlap.” In 26th Canadian Conference on Computational Geometry,
155–61. Canadian Conference on Computational Geometry, 2014.
ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,”
in 26th Canadian Conference on Computational Geometry, Halifax, Canada,
2014, pp. 155–161.
ista: 'Iglesias Ham M, Kerber M, Uhler C. 2014. Sphere packing with limited overlap.
26th Canadian Conference on Computational Geometry. CCCG: Canadian Conference
on Computational Geometry, 155–161.'
mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” 26th
Canadian Conference on Computational Geometry, Canadian Conference on Computational
Geometry, 2014, pp. 155–61.
short: M. Iglesias Ham, M. Kerber, C. Uhler, in:, 26th Canadian Conference on Computational
Geometry, Canadian Conference on Computational Geometry, 2014, pp. 155–161.
conference:
end_date: 2014-08-13
location: Halifax, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2014-08-11
corr_author: '1'
date_created: 2018-12-11T11:55:12Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2025-01-20T13:57:24Z
day: '01'
department:
- _id: HeEd
- _id: CaUh
external_id:
arxiv:
- '1401.0468'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://cccg.ca/proceedings/2014/papers/paper23.pdf
month: '09'
oa: 1
oa_version: Preprint
page: 155-161
publication: 26th Canadian Conference on Computational Geometry
publication_status: published
publisher: Canadian Conference on Computational Geometry
publist_id: '5064'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sphere packing with limited overlap
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2043'
abstract:
- lang: eng
text: Persistent homology is a popular and powerful tool for capturing topological
features of data. Advances in algorithms for computing persistent homology have
reduced the computation time drastically – as long as the algorithm does not exhaust
the available memory. Following up on a recently presented parallel method for
persistence computation on shared memory systems [1], we demonstrate that a simple
adaption of the standard reduction algorithm leads to a variant for distributed
systems. Our algorithmic design ensures that the data is distributed over the
nodes without redundancy; this permits the computation of much larger instances
than on a single machine. Moreover, we observe that the parallelism at least compensates
for the overhead caused by communication between nodes, and often even speeds
up the computation compared to sequential and even parallel shared memory algorithms.
In our experiments, we were able to compute the persistent homology of filtrations
with more than a billion (109) elements within seconds on a cluster with 32 nodes
using less than 6GB of memory per node.
article_processing_charge: No
arxiv: 1
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. Distributed computation of persistent homology.
In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering
and Experiments. Society for Industrial and Applied Mathematics; 2014:31-38.
doi:10.1137/1.9781611973198.4'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation
of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of
the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland,
USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4'
chicago: Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation
of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering
and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society
for Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.
ieee: U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent
homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments,
Portland, USA, 2014, pp. 31–38.
ista: 'Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent
homology. Proceedings of the Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, 31–38.'
mla: Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings
of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch
and Ulrich Meyer, Society for Industrial and Applied Mathematics, 2014, pp. 31–38,
doi:10.1137/1.9781611973198.4.
short: U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings
of the Workshop on Algorithm Engineering and Experiments, Society for Industrial
and Applied Mathematics, 2014, pp. 31–38.
conference:
end_date: 2014-01-05
location: Portland, USA
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2014-01-05
date_created: 2018-12-11T11:55:23Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2025-06-11T08:03:07Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973198.4
ec_funded: 1
editor:
- first_name: Catherine
full_name: ' McGeoch, Catherine'
last_name: ' McGeoch'
- first_name: Ulrich
full_name: Meyer, Ulrich
last_name: Meyer
external_id:
arxiv:
- '1310.0710'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.0710
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 38
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society for Industrial and Applied Mathematics
publist_id: '5008'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Distributed computation of persistent homology
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_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.
article_processing_charge: No
arxiv: 1
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.
corr_author: '1'
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-06-11T07:56:57Z
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
external_id:
arxiv:
- '1303.0477'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '1876'
abstract:
- lang: eng
text: We study densities of functionals over uniformly bounded triangulations of
a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay
triangulation if this is the case for finite sets.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai
full_name: Dolbilin, Nikolai
last_name: Dolbilin
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504
apa: Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals
on triangulations of delaunay sets. Moscow Mathematical Journal. Independent
University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin.
“Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal.
Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.
ieee: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations
of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent
University of Moscow, pp. 491–504, 2014.
ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.
mla: Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.”
Moscow Mathematical Journal, vol. 14, no. 3, Independent University of
Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.
short: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical
Journal 14 (2014) 491–504.
date_created: 2018-12-11T11:54:29Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2025-07-10T11:51:26Z
day: '01'
department:
- _id: HeEd
doi: 10.17323/1609-4514-2014-14-3-491-504
external_id:
arxiv:
- '1211.7053'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1211.7053
month: '07'
oa: 1
oa_version: Submitted Version
page: 491 - 504
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- 1609-3321
publication_status: published
publisher: Independent University of Moscow
publist_id: '5220'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functionals on triangulations of delaunay sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '1929'
abstract:
- lang: eng
text: We propose an algorithm for the generalization of cartographic objects that
can be used to represent maps on different scales.
acknowledgement: We would like to offer our special thanks to students of the Department
of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev
for participation in developing the program and assistance in preparation of test
data. This work was supported by grant 11.G34.31.0053 from the government of the
Russian Federation.
article_processing_charge: No
article_type: original
author:
- first_name: V V
full_name: Alexeev, V V
last_name: Alexeev
- first_name: V G
full_name: Bogaevskaya, V G
last_name: Bogaevskaya
- first_name: M M
full_name: Preobrazhenskaya, M M
last_name: Preobrazhenskaya
- first_name: A Y
full_name: Ukhalov, A Y
last_name: Ukhalov
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Olga
full_name: Yakimova, Olga
last_name: Yakimova
citation:
ama: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H,
Yakimova O. An algorithm for cartographic generalization that preserves global
topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8
apa: Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y.,
Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization
that preserves global topology. Journal of Mathematical Sciences. Springer.
https://doi.org/10.1007/s10958-014-2165-8
chicago: Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert
Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization
That Preserves Global Topology.” Journal of Mathematical Sciences. Springer,
2014. https://doi.org/10.1007/s10958-014-2165-8.
ieee: V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H.
Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that
preserves global topology,” Journal of Mathematical Sciences, vol. 203,
no. 6. Springer, pp. 754–760, 2014.
ista: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner
H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves
global topology. Journal of Mathematical Sciences. 203(6), 754–760.
mla: Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves
Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer,
2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.
short: V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner,
O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-11-16T00:00:00Z
date_updated: 2022-05-24T10:39:06Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/s10958-014-2165-8
intvolume: ' 203'
issue: '6'
language:
- iso: eng
month: '11'
oa_version: None
page: 754 - 760
publication: Journal of Mathematical Sciences
publication_identifier:
eissn:
- 1573-8795
issn:
- 1072-3374
publication_status: published
publisher: Springer
publist_id: '5165'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An algorithm for cartographic generalization that preserves global topology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2014'
...
---
_id: '1930'
abstract:
- lang: eng
text: (Figure Presented) Data acquisition, numerical inaccuracies, and sampling
often introduce noise in measurements and simulations. Removing this noise is
often necessary for efficient analysis and visualization of this data, yet many
denoising techniques change the minima and maxima of a scalar field. For example,
the extrema can appear or disappear, spatially move, and change their value. This
can lead to wrong interpretations of the data, e.g., when the maximum temperature
over an area is falsely reported being a few degrees cooler because the denoising
method is unaware of these features. Recently, a topological denoising technique
based on a global energy optimization was proposed, which allows the topology-controlled
denoising of 2D scalar fields. While this method preserves the minima and maxima,
it is constrained by the size of the data. We extend this work to large 2D data
and medium-sized 3D data by introducing a novel domain decomposition approach.
It allows processing small patches of the domain independently while still avoiding
the introduction of new critical points. Furthermore, we propose an iterative
refinement of the solution, which decreases the optimization energy compared to
the previous approach and therefore gives smoother results that are closer to
the input. We illustrate our technique on synthetic and real-world 2D and 3D data
sets that highlight potential applications.
acknowledgement: RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship;
MPC-VCC
article_processing_charge: No
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Alec
full_name: Jacobson, Alec
last_name: Jacobson
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans
full_name: Seidel, Hans
last_name: Seidel
- first_name: Olga
full_name: Sorkine Hornung, Olga
last_name: Sorkine Hornung
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594.
doi:10.1109/TVCG.2014.2346432
apa: Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O.,
& Weinkauf, T. (2014). Fast and memory-efficient topological denoising of
2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics.
IEEE. https://doi.org/10.1109/TVCG.2014.2346432
chicago: Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine
Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics.
IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.
ieee: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and
T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar
fields,” IEEE Transactions on Visualization and Computer Graphics, vol.
20, no. 12. IEEE, pp. 2585–2594, 2014.
ista: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.
mla: Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics,
vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.
short: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T.
Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-12-31T00:00:00Z
date_updated: 2025-09-29T12:11:45Z
day: '31'
department:
- _id: HeEd
doi: 10.1109/TVCG.2014.2346432
external_id:
isi:
- '000344991700104'
intvolume: ' 20'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2585 - 2594
publication: IEEE Transactions on Visualization and Computer Graphics
publication_status: published
publisher: IEEE
publist_id: '5164'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fast and memory-efficient topological denoising of 2D and 3D scalar fields
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 20
year: '2014'
...
---
_id: '10817'
abstract:
- lang: eng
text: The Morse-Smale complex can be either explicitly or implicitly represented.
Depending on the type of representation, the simplification of the Morse-Smale
complex works differently. In the explicit representation, the Morse-Smale complex
is directly simplified by explicitly reconnecting the critical points during the
simplification. In the implicit representation, on the other hand, the Morse-Smale
complex is given by a combinatorial gradient field. In this setting, the simplification
changes the combinatorial flow, which yields an indirect simplification of the
Morse-Smale complex. The topological complexity of the Morse-Smale complex is
reduced in both representations. However, the simplifications generally yield
different results. In this chapter, we emphasize properties of the two representations
that cause these differences. We also provide a complexity analysis of the two
schemes with respect to running time and memory consumption.
acknowledgement: This research is supported and funded by the Digiteo unTopoVis project,
the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.
article_processing_charge: No
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans-Peter
full_name: Seidel, Hans-Peter
last_name: Seidel
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification
of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds.
Topological Methods in Data Analysis and Visualization III. Mathematics
and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9'
apa: 'Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes
on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V.
Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9'
chicago: 'Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf.
“Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods
in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid
Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization.
Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.'
ieee: 'D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the
simplification of the Morse-Smale complex,” in Topological Methods in Data
Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R.
Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.'
ista: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification
of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization
III. , 135–150.'
mla: Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.”
Topological Methods in Data Analysis and Visualization III., edited by
Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.
short: D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer,
I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis
and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.
date_created: 2022-03-04T08:33:57Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_9
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
month: '03'
oa_version: None
page: 135-150
place: Cham
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_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Notes on the simplification of the Morse-Smale complex
type: book_chapter
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10886'
abstract:
- lang: eng
text: We propose a method for visualizing two-dimensional symmetric positive definite
tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the
heat kernel and was originally introduced as an isometry invariant shape signature.
Each positive definite tensor field defines a Riemannian manifold by considering
the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply
the definition of the HKS. The resulting scalar quantity is used for the visualization
of tensor fields. The HKS is closely related to the Gaussian curvature of the
Riemannian manifold and the time parameter of the heat kernel allows a multiscale
analysis in a natural way. In this way, the HKS represents field related scale
space properties, enabling a level of detail analysis of tensor fields. This makes
the HKS an interesting new scalar quantity for tensor fields, which differs significantly
from usual tensor invariants like the trace or the determinant. A method for visualization
and a numerical realization of the HKS for tensor fields is proposed in this chapter.
To validate the approach we apply it to some illustrating simple examples as isolated
critical points and to a medical diffusion tensor data set.
acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
full_name: Zobel, Valentin
last_name: Zobel
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
citation:
ama: 'Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. In: Topological
Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional
symmetric positive definite tensor fields using the heat kernel signature. In
Topological Methods in Data Analysis and Visualization III (pp. 249–262).
Springer. https://doi.org/10.1007/978-3-319-04099-8_16
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional
Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In
Topological Methods in Data Analysis and Visualization III , 249–62. Springer,
2014. https://doi.org/10.1007/978-3-319-04099-8_16.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature,” in Topological
Methods in Data Analysis and Visualization III , 2014, pp. 249–262.
ista: Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. Topological Methods
in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.
mla: Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive
Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods
in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis
and Visualization III , Springer, 2014, pp. 249–262.
date_created: 2022-03-18T13:05:39Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2023-09-05T14:13:16Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_16
language:
- iso: eng
month: '03'
oa_version: None
page: 249-262
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualization of two-dimensional symmetric positive definite tensor fields
using the heat kernel signature
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10892'
abstract:
- lang: eng
text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements,
which yield a planar set of pseudo-line segments such that only matching-partners
are adjacent. By translating the planar matching problem into a corresponding
stable roommates problem we show that such matchings always exist.\r\nUsing our
new framework, we establish, for the first time, a complete, rigorous definition
of weighted straight skeletons, which are based on a so-called wavefront propagation
process. We present a generalized and unified approach to treat structural changes
in the wavefront that focuses on the restoration of weak planarity by finding
planar matchings."
acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton
Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature;
2014:117-127. doi:10.1007/978-3-319-13075-0_10'
apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted
straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889,
pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10'
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014,
8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea,
2014, vol. 8889, pp. 117–127.
ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight
skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium
on Algorithms and Computation, LNCS, vol. 8889, 117–127.'
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014,
pp. 117–27, doi:10.1007/978-3-319-13075-0_10.
short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC
2014, Springer Nature, 2014, pp. 117–127.
conference:
end_date: 2014-12-17
location: Jeonju, Korea
name: 'ISAAC: International Symposium on Algorithms and Computation'
start_date: 2014-12-15
corr_author: '1'
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2025-09-29T13:22:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
external_id:
isi:
- '000354865900010'
intvolume: ' 8889'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 117-127
publication: 25th International Symposium, ISAAC 2014
publication_identifier:
eisbn:
- '9783319130750'
eissn:
- 1611-3349
isbn:
- '9783319130743'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '481'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Planar matchings for weighted straight skeletons
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 8889
year: '2014'
...
---
_id: '10893'
abstract:
- lang: eng
text: Saddle periodic orbits are an essential and stable part of the topological
skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm
to robustly extract these features. In this chapter, we present a novel technique
to extract saddle periodic orbits. Exploiting the analytic properties of such
an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent
(FTLE) that indicates its presence. Using persistent homology, we can then extract
the robust cycles of this field. These cycles thereby represent the saddle periodic
orbits of the given vector field. We discuss the different existing FTLE approximation
schemes regarding their applicability to this specific problem and propose an
adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate
our method using simple analytic vector field data.
acknowledgement: First, we thank the reviewers of this paper for their ideas and critical
comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions.
This research is supported by the European Commission under the TOPOSYS project
FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the
European Science Foundation under the ACAT Research Network Program.
article_processing_charge: No
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Wieland
full_name: Reich, Wieland
last_name: Reich
- first_name: Gerik
full_name: Scheuermann, Gerik
last_name: Scheuermann
citation:
ama: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of
saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization.
Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4'
apa: 'Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward
the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci,
& R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization
III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4'
chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward
the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis
and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014.
https://doi.org/10.1007/978-3-319-04099-8_4.'
ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction
of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization
III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham:
Springer, 2014, pp. 55–69.'
ista: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction
of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization
III . vol. 1, 55–69.'
mla: Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological
Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer
et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.
short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I.
Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III , Springer, Cham, 2014, pp. 55–69.
date_created: 2022-03-21T07:11:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_4
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
intvolume: ' 1'
language:
- iso: eng
month: '03'
oa_version: None
page: 55-69
place: Cham
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_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Toward the extraction of saddle periodic orbits
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2014'
...
---
_id: '10894'
abstract:
- lang: eng
text: PHAT is a C++ library for the computation of persistent homology by matrix
reduction. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. This makes PHAT
a versatile platform for experimenting with algorithmic ideas and comparing them
to state of the art implementations.
article_processing_charge: No
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
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
last_name: Wagner
citation:
ama: 'Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms
Toolbox. In: ICMS 2014: International Congress on Mathematical Software.
Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143.
doi:10.1007/978-3-662-44199-2_24'
apa: 'Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent
Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical
Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-662-44199-2_24'
chicago: 'Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT
– Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress
on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer
Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.'
ieee: 'U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology
Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software,
Seoul, South Korea, 2014, vol. 8592, pp. 137–143.'
ista: 'Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology
Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software.
ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.'
mla: 'Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS
2014: International Congress on Mathematical Software, vol. 8592, Springer
Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.'
short: 'U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International
Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg,
2014, pp. 137–143.'
conference:
end_date: 2014-08-09
location: Seoul, South Korea
name: 'ICMS: International Congress on Mathematical Software'
start_date: 2014-08-05
date_created: 2022-03-21T07:12:16Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2025-10-01T07:39:50Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-662-44199-2_24
intvolume: ' 8592'
language:
- iso: eng
month: '09'
oa_version: None
page: 137-143
place: Berlin, Heidelberg
publication: 'ICMS 2014: International Congress on Mathematical Software'
publication_identifier:
eisbn:
- '9783662441992'
eissn:
- 1611-3349
isbn:
- '9783662441985'
issn:
- 0302-9743
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
related_material:
record:
- id: '1433'
relation: later_version
status: public
scopus_import: '1'
series_title: LNCS
status: public
title: PHAT – Persistent Homology Algorithms Toolbox
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 8592
year: '2014'
...
---
_id: '2153'
abstract:
- lang: eng
text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise
finite dimensional persistence modules to a matching between the barcodes of M
and N. Our main result is that, in a precise sense, the quality of this matching
is tightly controlled by the lengths of the longest intervals in the barcodes
of ker f and coker f . As an immediate corollary, we obtain a new proof of the
algebraic stability theorem for persistence barcodes [5, 9], a fundamental result
in the theory of persistent homology. In contrast to previous proofs, ours shows
explicitly how a δ-interleaving morphism between two persistence modules induces
a δ-matching between the barcodes of the two modules. Our main result also specializes
to a structure theorem for submodules and quotients of persistence modules. Copyright
is held by the owner/author(s).'
article_processing_charge: No
arxiv: 1
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: Lesnick, Michael
last_name: Lesnick
citation:
ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability
of persistence. In: Proceedings of the Annual Symposium on Computational Geometry.
ACM; 2014:355-364. doi:10.1145/2582112.2582168'
apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the
algebraic stability of persistence. In Proceedings of the Annual Symposium
on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168'
chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and
the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium
on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.
ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic
stability of persistence,” in Proceedings of the Annual Symposium on Computational
Geometry, Kyoto, Japan, 2014, pp. 355–364.
ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic
stability of persistence. Proceedings of the Annual Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 355–364.'
mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the
Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on
Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.
short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 355–364.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-06-11T07:57:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
external_id:
arxiv:
- '1311.3681'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.3681
month: '06'
oa: 1
oa_version: Submitted Version
page: 355 - 364
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4853'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Induced matchings of barcodes and the algebraic stability of persistence
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2155'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a positive radius, we study the Čech,
Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete
Morse theory. We prove that the latter three complexes are simple-homotopy equivalent.
Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data. Copyright is held by the owner/author(s).
acknowledgement: This research is partially supported by ESF under the ACAT Research
Network Programme, and by the Russian Government under mega project 11.G34.31.0053
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations.
In: Proceedings of the Annual Symposium on Computational Geometry. ACM;
2014:484-490. doi:10.1145/2582112.2582167'
apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay
filtrations. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167'
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational
Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.
ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,”
in Proceedings of the Annual Symposium on Computational Geometry, Kyoto,
Japan, 2014, pp. 484–490.
ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations.
Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, 484–490.'
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Filtrations.” Proceedings of the Annual Symposium on Computational Geometry,
ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.
short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 484–490.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
corr_author: '1'
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-06-11T07:58:27Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1312.1231
month: '06'
oa: 1
oa_version: Submitted Version
page: 484 - 490
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4851'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The morse theory of Čech and Delaunay filtrations
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2156'
abstract:
- lang: eng
text: We propose a metric for Reeb graphs, called the functional distortion distance.
Under this distance, the Reeb graph is stable against small changes of input functions.
At the same time, it remains discriminative at differentiating input functions.
In particular, the main result is that the functional distortion distance between
two Reeb graphs is bounded from below by the bottleneck distance between both
the ordinary and extended persistence diagrams for appropriate dimensions. As
an application of our results, we analyze a natural simplification scheme for
Reeb graphs, and show that persistent features in Reeb graph remains persistent
under simplification. Understanding the stability of important features of the
Reeb graph under simplification is an interesting problem on its own right, and
critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Xiaoyin
full_name: Ge, Xiaoyin
last_name: Ge
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings
of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169'
apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb
graphs. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169'
chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb
Graphs.” In Proceedings of the Annual Symposium on Computational Geometry,
464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.
ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in
Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan,
2014, pp. 464–473.
ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings
of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, 464–473.'
mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings
of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73,
doi:10.1145/2582112.2582169.
short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 464–473.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-06-11T07:58:42Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582169
ec_funded: 1
external_id:
arxiv:
- '1307.2839'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.2839
month: '06'
oa: 1
oa_version: Submitted Version
page: 464 - 473
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4850'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Measuring distance between Reeb graphs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2177'
abstract:
- lang: eng
text: We give evidence for the difficulty of computing Betti numbers of simplicial
complexes over a finite field. We do this by reducing the rank computation for
sparse matrices with to non-zero entries to computing Betti numbers of simplicial
complexes consisting of at most a constant times to simplices. Together with the
known reduction in the other direction, this implies that the two problems have
the same computational complexity.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Salman
full_name: Parsa, Salman
id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87
last_name: Parsa
citation:
ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers
reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11'
apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity
of betti numbers reductions from matrix rank. In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM.
https://doi.org/10.1137/1.9781611973402.11'
chicago: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity
of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.
ieee: H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers
reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.
ista: 'Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers
reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.'
mla: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of
Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.
short: H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, SIAM, 2014, pp. 152–160.
conference:
end_date: 2014-01-07
location: Portland, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2014-01-05
corr_author: '1'
date_created: 2018-12-11T11:56:09Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2024-10-09T20:55:33Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973402.11
language:
- iso: eng
month: '01'
oa_version: None
page: 152 - 160
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_status: published
publisher: SIAM
publist_id: '4805'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the computational complexity of betti numbers reductions from matrix rank
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2184'
abstract:
- lang: eng
text: 'Given topological spaces X,Y, a fundamental problem of algebraic topology
is understanding the structure of all continuous maps X→ Y. We consider a computational
version, where X,Y are given as finite simplicial complexes, and the goal is to
compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem
in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected;
in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical
tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and
simplicial sets) with algorithmic tools from effective algebraic topology (locally
effective simplicial sets and objects with effective homology). In contrast, [X,Y]
is known to be uncomputable for general X,Y, since for X = S1 it includes a well
known undecidable problem: testing triviality of the fundamental group of Y. In
follow-up papers, the algorithm is shown to run in polynomial time for d fixed,
and extended to other problems, such as the extension problem, where we are given
a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or
computing the Z2-index-everything in the stable range. Outside the stable range,
the extension problem is undecidable.'
acknowledgement: The research by M. K. was supported by project GAUK 49209. The research
by M. K. was also supported by project 1M0545 by the Ministry of Education of the
Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague
(project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss
National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).
article_number: '17 '
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Francis
full_name: Sergeraert, Francis
last_name: Sergeraert
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing
all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629
apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner,
U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629
chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek,
and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM.
ACM, 2014. https://doi.org/10.1145/2597629.
ieee: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner,
“Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3.
ACM, 2014.
ista: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing
all maps into a sphere. Journal of the ACM. 61(3), 17.
mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the
ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.
short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal
of the ACM 61 (2014).
date_created: 2018-12-11T11:56:12Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2025-09-29T11:34:15Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2597629
external_id:
arxiv:
- '1105.6257'
isi:
- '000337201400003'
intvolume: ' 61'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1105.6257
month: '05'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '4797'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing all maps into a sphere
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 61
year: '2014'
...
---
_id: '6853'
abstract:
- lang: eng
text: This monograph presents a short course in computational geometry and topology.
In the first part the book covers Voronoi diagrams and Delaunay triangulations,
then it presents the theory of alpha complexes which play a crucial role in biology.
The central part of the book is the homology theory and their computation, including
the theory of persistence which is indispensable for applications, e.g. shape
reconstruction. The target audience comprises researchers and practitioners in
mathematics, biology, neuroscience and computer science, but the book may also
be beneficial to graduate students of these fields.
alternative_title:
- SpringerBriefs in Applied Sciences and Technology
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Edelsbrunner H. A Short Course in Computational Geometry and Topology.
1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0'
apa: 'Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology
(1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0'
chicago: 'Edelsbrunner, Herbert. A Short Course in Computational Geometry and
Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham:
Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.'
ieee: 'H. Edelsbrunner, A Short Course in Computational Geometry and Topology,
1st ed. Cham: Springer Nature, 2014.'
ista: 'Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology
1st ed., Cham: Springer Nature, IX, 110p.'
mla: Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology.
1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0.
short: H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st
ed., Springer Nature, Cham, 2014.
date_created: 2019-09-06T09:22:33Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2022-03-04T07:47:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-05957-0
edition: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: IX, 110
place: Cham
publication_identifier:
eisbn:
- 9-783-3190-5957-0
eissn:
- 2191-5318
isbn:
- 9-783-3190-5956-3
issn:
- 2191-530X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- description: available as eBook via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106
- description: available via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842
scopus_import: '1'
series_title: SpringerBriefs in Applied Sciences and Technology
status: public
title: A Short Course in Computational Geometry and Topology
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2255'
abstract:
- lang: eng
text: Motivated by applications in biology, we present an algorithm for estimating
the length of tube-like shapes in 3-dimensional Euclidean space. In a first step,
we combine the tube formula of Weyl with integral geometric methods to obtain
an integral representation of the length, which we approximate using a variant
of the Koksma-Hlawka Theorem. In a second step, we use tools from computational
topology to decrease the dependence on small perturbations of the shape. We present
computational experiments that shed light on the stability and the convergence
rate of our algorithm.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal
of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x
apa: Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like
shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer,
2014. https://doi.org/10.1007/s10851-013-0468-x.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp.
164–177, 2014.
ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes.
Journal of Mathematical Imaging and Vision. 50(1), 164–177.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer,
2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.
short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision
50 (2014) 164–177.
corr_author: '1'
date_created: 2018-12-11T11:56:36Z
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title: Stable length estimates of tube-like shapes
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...
---
_id: '2807'
abstract:
- lang: eng
text: 'We consider several basic problems of algebraic topology, with connections
to combinatorial and geometric questions, from the point of view of computational
complexity. The extension problem asks, given topological spaces X; Y , a subspace
A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X
→ Y . For computational purposes, we assume that X and Y are represented as finite
simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map.
In this generality the problem is undecidable, as follows from Novikov''s result
from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study
the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected;
informally, this means that Y has \no holes up to dimension k-1" (a basic
example of such a Y is the sphere Sk). We prove that, on the one hand, this problem
is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2,
we obtain an algorithm that solves the extension problem in polynomial time assuming
Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides
a classification of all extensions up to homotopy (continuous deformation). This
relies on results of our SODA 2012 paper, and the main new ingredient is a machinery
of objects with polynomial-time homology, which is a polynomial-time analog of
objects with effective homology developed earlier by Sergeraert et al. We also
consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected
Y . Their computability was established by Brown in 1957; we show that πk(Y )
can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick
proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where
Y is a cell complex with certain rather compact encoding. We strengthen his result
to #P-hardness for Y given as a simplicial complex. '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps:
Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of
Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683'
apa: 'Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013).
Extending continuous maps: Polynomiality and undecidability. In 45th Annual
ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United
States: ACM. https://doi.org/10.1145/2488608.2488683'
chicago: 'Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner.
“Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual
ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.'
ieee: 'M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous
maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory
of computing, Palo Alto, CA, United States, 2013, pp. 595–604.'
ista: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous
maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of
computing. STOC: Symposium on the Theory of Computing, 595–604.'
mla: 'Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.”
45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604,
doi:10.1145/2488608.2488683.'
short: M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual
ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.
conference:
end_date: 2013-06-04
location: Palo Alto, CA, United States
name: 'STOC: Symposium on the Theory of Computing'
start_date: 2013-06-01
date_created: 2018-12-11T11:59:42Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:51Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2488608.2488683
file:
- access_level: open_access
checksum: 06c2ce5c1135fbc1f71ca15eeb242dcf
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creator: system
date_created: 2018-12-12T10:14:29Z
date_updated: 2020-07-14T12:45:48Z
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file_name: IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf
file_size: 447945
relation: main_file
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has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 595 - 604
publication: 45th Annual ACM Symposium on theory of computing
publication_status: published
publisher: ACM
publist_id: '4078'
pubrep_id: '533'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Extending continuous maps: Polynomiality and undecidability'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...