Alpha Shape Theory Extended

Project Period: 2018-07-01 – 2023-06-30
Externally Funded
Acronym
ALPHA
Principal Investigator
Herbert Edelsbrunner
Department(s)
Edelsbrunner Group
Grant Number
788183
Funder
EC/H2020

37 Publications

2024 |Published| Conference Paper | IST-REx-ID: 15012 | OA
Decomposition of geometric graphs into star-forests
J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 
2024 |Published| Thesis | IST-REx-ID: 15094 | OA
Persistence and Morse theory for discrete geometric structures
S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.
[Published Version] View | Files available | DOI
 
2024 |Published| Conference Paper | IST-REx-ID: 15093 | OA
Dynamically maintaining the persistent homology of time series
S. Cultrera di Montesano, H. Edelsbrunner, M.H. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.
[Preprint] View | Files available | DOI | Download Preprint (ext.) | arXiv
 
2024 |Published| Journal Article | IST-REx-ID: 15380 | OA
Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2024).
[Published Version] View | Files available | DOI | Download Published Version (ext.)
 
2024 |Published| Conference Paper | IST-REx-ID: 17144 | OA
The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms
H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version] View | Files available | DOI | arXiv
 
2024 |Epub ahead of print| Journal Article | IST-REx-ID: 17149 | OA
Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
[Published Version] View | DOI | Download Published Version (ext.) | arXiv
 
2024 |Published| Conference Paper | IST-REx-ID: 17146 | OA
Maximum Betti numbers of Čech complexes
H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version] View | Files available | DOI | arXiv
 
2024 |Published| Conference Paper | IST-REx-ID: 17170 | OA
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds
D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.
[Published Version] View | Files available | DOI | arXiv
 
2024 |Published| Journal Article | IST-REx-ID: 17190 | OA
Brillouin zones of integer lattices and their perturbations
H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 
2023 |Published| Journal Article | IST-REx-ID: 12086 | OA
A simple algorithm for higher-order Delaunay mosaics and alpha shapes
H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
[Published Version] View | Files available | DOI | WoS
 
2023 |Published| Journal Article | IST-REx-ID: 12544 | OA
Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives
P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.
[Published Version] View | Files available | DOI | WoS | PubMed | Europe PMC
 
2023 |Epub ahead of print| Journal Article | IST-REx-ID: 14345 | OA
On angles in higher order Brillouin tessellations and related tilings in the plane
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).
[Published Version] View | DOI | Download Published Version (ext.) | WoS | arXiv
 
2023 |Epub ahead of print| Journal Article | IST-REx-ID: 13182 | OA
Geometric characterization of the persistence of 1D maps
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023).
[Published Version] View | Files available | DOI
 
2022 |Published| Conference Paper | IST-REx-ID: 11428 | OA
A cautionary tale: Burning the medial axis is unstable
E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
[Published Version] View | Files available | DOI
 
2022 |Published| Book Chapter | IST-REx-ID: 11440 | OA
The persistent homology of dual digital image constructions
B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 
2022 |Published| Journal Article | IST-REx-ID: 7791 | OA
When different norms lead to same billiard trajectories?
A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.
[Published Version] View | Files available | DOI | arXiv
 
2022 |Submitted| Journal Article | IST-REx-ID: 11660 | OA
A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).
[Submitted Version] View | Files available
 
2022 |Submitted| Preprint | IST-REx-ID: 15090 | OA
On the size of chromatic Delaunay mosaics
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint] View | Files available | Download Preprint (ext.) | arXiv
 
2022 |Submitted| Journal Article | IST-REx-ID: 11658 | OA
Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).
[Submitted Version] View | Files available
 
2022 |Published| Journal Article | IST-REx-ID: 8538 | OA
Billiards in ellipses revisited
A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics 8 (2022) 1313–1327.
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 

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