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282 Publications
2025 | Published | Thesis | IST-REx-ID: 18979 | 
Structures and computations in topological data analysis
O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.
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O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.
2025 | Published | Journal Article | IST-REx-ID: 18626 |
Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
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H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
2024 | Published | Journal Article | IST-REx-ID: 18604 |
Removing popular faces in curve arrangements
P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.
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P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.
2024 | Published | Journal Article | IST-REx-ID: 13182 |
Geometric characterization of the persistence of 1D maps
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
2024 | Published | Journal Article | IST-REx-ID: 15247 |
Odd-sunflowers
P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).
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P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).
2024 | Published | Journal Article | IST-REx-ID: 15380 |
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 8 (2024) 557–578.
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
2024 | Published | Thesis | IST-REx-ID: 18667 |
New methods for applying topological data analysis to materials science
T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.
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T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.
2024 | Draft | Preprint | IST-REx-ID: 18673 |
Merge trees of periodic filtrations
H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
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H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
2024 | Published | Conference Paper | IST-REx-ID: 15093 |
Dynamically maintaining the persistent homology of time series
S. Cultrera di Montesano, H. Edelsbrunner, M. 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.
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S. Cultrera di Montesano, H. Edelsbrunner, M. 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.
2024 | Published | Thesis | IST-REx-ID: 15094 |
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.
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S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.
2024 | Draft | Preprint | IST-REx-ID: 18981 |
Discrete microlocal Morse theory
A. Brown, O. Draganov, ArXiv (n.d.).
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A. Brown, O. Draganov, ArXiv (n.d.).
2024 | Draft | Preprint | IST-REx-ID: 15091 |
Chromatic alpha complexes
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
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S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2024 | Published | Conference Paper | IST-REx-ID: 18998 |
The shape of word embeddings: Quantifying non-isometry with topological data analysis
O. Draganov, S. Skiena, in:, Findings of the Association for Computational Linguistics: EMNLP 2024, Association for Computational Linguistics, 2024, pp. 12080–12099.
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O. Draganov, S. Skiena, in:, Findings of the Association for Computational Linguistics: EMNLP 2024, Association for Computational Linguistics, 2024, pp. 12080–12099.
2024 | Submitted | Preprint | IST-REx-ID: 18999 |
Chromatic topological data analysis
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
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S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2024 | Published | Journal Article | IST-REx-ID: 14345 |
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 72 (2024) 29–48.
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H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
2024 | Published | Conference Paper | IST-REx-ID: 17144 |
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.
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H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Conference Paper | IST-REx-ID: 17145 |
Grid peeling of parabolas
G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Conference Paper | IST-REx-ID: 17146 |
Maximum Betti numbers of Čech complexes
H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Epub ahead of print | Journal Article | IST-REx-ID: 17149 |
Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
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H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
2024 | Published | Conference Paper | IST-REx-ID: 17170 |
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.
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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.