16 Search Results for "Wagner, Hubert"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.32
Tensor Computation of Euler Characteristic Functions and Transforms

Authors: Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary, and Eli Quist

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU computation or do not scale to higher-dimensional settings. In this work, we present a tensor-based framework for computing such topological descriptors which is highly optimized for GPU architectures and works in full generality across simplicial and cubical complexes of arbitrary dimension. Experimentally, the framework demonstrates significant speedups over existing methods when computing the WECT and ECF across a variety of two- and three-dimensional datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT.
Cite as

Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary, and Eli Quist. Tensor Computation of Euler Characteristic Functions and Transforms. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{cisewskikehe_et_al:LIPIcs.SoCG.2026.32,
  author =	{Cisewski-Kehe, Jessi and Fasy, Brittany Terese and McCleary, Alexander and Quist, Eli},
  title =	{{Tensor Computation of Euler Characteristic Functions and Transforms}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.32},
  URN =		{urn:nbn:de:0030-drops-258380},
  doi =		{10.4230/LIPIcs.SoCG.2026.32},
  annote =	{Keywords: Topological data analysis, weighted Euler characteristic transform, Euler characteristic function, tensor computation, GPU computation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.72
Topological Simplification Guided by Forbidden Regions

Authors: Jakub Leśkiewicz, Bartosz Furmanek, Michał Lipiński, and Dmitriy Morozov

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c⋅n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex.
Cite as

Jakub Leśkiewicz, Bartosz Furmanek, Michał Lipiński, and Dmitriy Morozov. Topological Simplification Guided by Forbidden Regions. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{leskiewicz_et_al:LIPIcs.SoCG.2026.72,
  author =	{Le\'{s}kiewicz, Jakub and Furmanek, Bartosz and Lipi\'{n}ski, Micha{\l} and Morozov, Dmitriy},
  title =	{{Topological Simplification Guided by Forbidden Regions}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{72:1--72:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.72},
  URN =		{urn:nbn:de:0030-drops-258797},
  doi =		{10.4230/LIPIcs.SoCG.2026.72},
  annote =	{Keywords: persistent homology, topological simplification, depth posets}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.94
Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds

Authors: Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We propose a novel geometric-topological descriptor called a mixup barcode. Intuitively, it characterizes the shape of a point cloud as well as its spatial relationship with another point cloud embedded in the same ambient space. More technically, it enriches a standard persistence barcode with information on the image persistent homology. In three dimensions it captures natural spatial relationships like overlap and surrounding; in higher dimensions more intricate spatial relationships are captured. We provide a theoretical setup and a simple algorithm for mixup barcodes. As a proof of concept, we explore data arising in a geometric-topological problem from machine learning. Specifically, we take first steps towards verifying a hypothesis stating that geometric-topological relationships within intermediate point cloud representations in an artificial neural network can hinder its training. More broadly, our experiments suggest that mixup barcodes are useful for characterizing spatial relationships and spatial interactions (i.e. the evolution of spatial relationships) that are hard to directly visualize or capture using standard methods.
Cite as

Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik. Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 94:1-94:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{wagner_et_al:LIPIcs.SoCG.2026.94,
  author =	{Wagner, Hubert and Arustamyan, Nickolas and Wheeler, Matthew and Bubenik, Peter},
  title =	{{Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{94:1--94:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.94},
  URN =		{urn:nbn:de:0030-drops-259009},
  doi =		{10.4230/LIPIcs.SoCG.2026.94},
  annote =	{Keywords: mixup barcode, persistent homology, persistence barcode, persistence diagram, image persistent homology, image persistence, deep learning, multilayer perceptron, topology of neural network embeddings, disentanglement}
}
Artifact
Software
DOI: 10.4230/artifacts.26095
hubwag/Mixup-SoCG26

Authors: Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik

Abstract
Cite as

Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, Peter Bubenik. hubwag/Mixup-SoCG26 (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-26095,
   title = {{hubwag/Mixup-SoCG26}}, 
   author = {Wagner, Hubert and Arustamyan, Nickolas and Wheeler, Matthew and Bubenik, Peter},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:9b75232380440dc7556b698dd1b7d07882a61fac}{\texttt{swh:1:dir:9b75232380440dc7556b698dd1b7d07882a61fac}} (visited on 2026-05-27)},
   url = {https://github.com/hubwag/Mixup-SoCG26},
   doi = {10.4230/artifacts.26095},
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.48
Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract)

Authors: Henry Förster, Stephen Kobourov, Jacob Miller, and Johannes Zink

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A strengthened version of Harborth’s well-known conjecture - known as Kleber’s conjecture - states that every planar graph admits a planar straight-line drawing where every edge has integer length and each vertex is restricted to the integer grid. Positive results for Kleber’s conjecture are known for planar 3-regular graphs, for planar graphs that have maximum degree 4, and for planar 3-trees. However, all but one of the existing results are existential and do not provide bounds on the required grid size. We provide polynomial-time algorithms for computing crossing-free straight-line drawings of trees and cactus graphs with integer edge lengths and integer vertex position on polynomial-size integer grids. We also give an historic overview of planar straight-line graph drawing results.
Cite as

Henry Förster, Stephen Kobourov, Jacob Miller, and Johannes Zink. Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 48:1-48:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{forster_et_al:LIPIcs.GD.2025.48,
  author =	{F\"{o}rster, Henry and Kobourov, Stephen and Miller, Jacob and Zink, Johannes},
  title =	{{Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{48:1--48:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.48},
  URN =		{urn:nbn:de:0030-drops-250349},
  doi =		{10.4230/LIPIcs.GD.2025.48},
  annote =	{Keywords: Harborth’s conjecture, tree drawings, cactus drawings, grid drawings}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.56
Using Reinforcement Learning to Optimize the Global and Local Crossing Number (Poster Abstract)

Authors: Timo Brand, Henry Förster, Stephen Kobourov, Robin Schukrafft, Markus Wallinger, and Johannes Zink

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively. An agent learns how to move a vertex based on a given observation vector. The agent receives feedback in the form of local reward signals tied to crossing reduction. To generate an initial layout, we use a stress-based graph-drawing algorithm. We compare our method against force- and stress-based baseline algorithms as well as three established algorithms for global crossing minimization on a suite of benchmark graphs. The experiments show mixed results: our current algorithm is mainly competitive for the local crossing number.
Cite as

Timo Brand, Henry Förster, Stephen Kobourov, Robin Schukrafft, Markus Wallinger, and Johannes Zink. Using Reinforcement Learning to Optimize the Global and Local Crossing Number (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 56:1-56:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{brand_et_al:LIPIcs.GD.2025.56,
  author =	{Brand, Timo and F\"{o}rster, Henry and Kobourov, Stephen and Schukrafft, Robin and Wallinger, Markus and Zink, Johannes},
  title =	{{Using Reinforcement Learning to Optimize the Global and Local Crossing Number}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{56:1--56:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.56},
  URN =		{urn:nbn:de:0030-drops-250420},
  doi =		{10.4230/LIPIcs.GD.2025.56},
  annote =	{Keywords: Reinforcement Learning, Crossing Minimization, Local Crossing Number}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.45
Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences

Authors: Tuyen Pham and Hubert Wagner

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to ℝ^d with the distance measured by an arbitrary Bregman divergence. Perhaps surprisingly, this shows that the triangle inequality is not necessary for correct pruning in Kd-trees. Second, we offer an efficient algorithm and C++ implementation for nearest neighbour search for decomposable Bregman divergences. The implementation supports the Kullback-Leibler divergence (relative entropy) which is a popular distance between probability vectors and is commonly used in statistics and machine learning. This is a step toward broadening the usage of computational geometry algorithms. Our benchmarks show that our implementation efficiently handles both exact and approximate nearest neighbour queries. Compared to a linear search, we achieve two orders of magnitude speedup for practical scenarios in dimension up to 100. Our solution is simpler and more efficient than competing methods.
Cite as

Tuyen Pham and Hubert Wagner. Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{pham_et_al:LIPIcs.WADS.2025.45,
  author =	{Pham, Tuyen and Wagner, Hubert},
  title =	{{Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.45},
  URN =		{urn:nbn:de:0030-drops-242766},
  doi =		{10.4230/LIPIcs.WADS.2025.45},
  annote =	{Keywords: Kd-tree, k-d tree, nearest neighbour search, Bregman divergence, decomposable Bregman divergence, KL divergence, relative entropy, cross entropy, Shannon’s entropy}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.39
Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points

Authors: Anupam Das and Abhishek De

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely unexplored. In recent work [Anupam Das and Abhishek De, 2024], a notation for non-deterministic finite automata (NFAs) was introduced, along with a sound and complete axiomatisation of their equational theory via right-linear algebras. In this paper, we extend that line of work to the setting of infinite words. In particular, we present a dualised syntax, yielding a notation for APAs based on right-linear lattice expressions, and provide a natural axiomatisation of their equational theory with respect to the standard language model of ω-regular languages. The design of this axiomatisation is guided by the theory of fixed point logics; in fact, the completeness factors cleanly through the completeness of the linear-time μ-calculus.
Cite as

Anupam Das and Abhishek De. Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{das_et_al:LIPIcs.MFCS.2025.39,
  author =	{Das, Anupam and De, Abhishek},
  title =	{{Right-Linear Lattices: An Algebraic Theory of \omega-Regular Languages, with Fixed Points}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.39},
  URN =		{urn:nbn:de:0030-drops-241461},
  doi =		{10.4230/LIPIcs.MFCS.2025.39},
  annote =	{Keywords: omega-languages, regular languages, fixed points, Kleene algebras, right-linear grammars}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.41
Decomposing Multiparameter Persistence Modules

Authors: Tamal K. Dey, Jan Jendrysiak, and Michael Kerber

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Dey and Xin (J.Appl.Comput.Top., 2022) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators and relations are distinctly graded. We extend their approach to work on all finitely presented modules and introduce several improvements that lead to significant speed-ups in practice. Our algorithm is fixed-parameter tractable with respect to the maximal number of relations of the same degree and with further optimisation we obtain an O(n³) time algorithm for interval-decomposable modules. In particular, we can decide interval-decomposability in this time. As a by-product to the proofs of correctness we develop a theory of parameter restriction for persistence modules. Our algorithm is implemented as a software library aida, the first to enable the decomposition of large inputs. We show its capabilities via extensive experimental evaluation.
Cite as

Tamal K. Dey, Jan Jendrysiak, and Michael Kerber. Decomposing Multiparameter Persistence Modules. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dey_et_al:LIPIcs.SoCG.2025.41,
  author =	{Dey, Tamal K. and Jendrysiak, Jan and Kerber, Michael},
  title =	{{Decomposing Multiparameter Persistence Modules}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.41},
  URN =		{urn:nbn:de:0030-drops-231939},
  doi =		{10.4230/LIPIcs.SoCG.2025.41},
  annote =	{Keywords: Topological Data Analysis, Multiparameter Persistence Modules, Persistence, Decomposition}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.68
Persistent (Co)Homology in Matrix Multiplication Time

Authors: Dmitriy Morozov and Primoz Skraba

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that persistence diagrams can be computed in matrix multiplication time for the more general case of zigzag persistent homology [Milosavljević et al., 2011], it is not clear how to extract cycle representatives, especially if specific representatives are desired. In this paper, we provide the same matrix multiplication bound for computing representatives for the two choices common in applications in the case of ordinary persistent (co)homology. We first provide a fast version of the reduction algorithm, which is simpler than the algorithm in [Milosavljević et al., 2011], but returns a different set of representatives than the standard algorithm [Edelsbrunner et al., 2002]. We then give a fast version of a variant called the row algorithm [De Silva et al., 2011], which returns the same representatives as the standard algorithm.
Cite as

Dmitriy Morozov and Primoz Skraba. Persistent (Co)Homology in Matrix Multiplication Time. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 68:1-68:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{morozov_et_al:LIPIcs.SoCG.2025.68,
  author =	{Morozov, Dmitriy and Skraba, Primoz},
  title =	{{Persistent (Co)Homology in Matrix Multiplication Time}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{68:1--68:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.68},
  URN =		{urn:nbn:de:0030-drops-232204},
  doi =		{10.4230/LIPIcs.SoCG.2025.68},
  annote =	{Keywords: persistent homology, matrix multiplication, cycle representatives}
}
Document
Academic Track
DOI: 10.4230/OASIcs.SAIA.2024.12
A View on Vulnerabilites: The Security Challenges of XAI (Academic Track)

Authors: Elisabeth Pachl, Fabian Langer, Thora Markert, and Jeanette Miriam Lorenz

Published in: OASIcs, Volume 126, Symposium on Scaling AI Assessments (SAIA 2024)

Abstract
Modern deep learning methods have long been considered as black-boxes due to their opaque decision-making processes. Explainable Artificial Intelligence (XAI), however, has turned the tables: it provides insight into how these models work, promoting transparency that is crucial for accountability. Yet, recent developments in adversarial machine learning have highlighted vulnerabilities in XAI methods, raising concerns about security, reliability and trustworthiness, particularly in sensitive areas like healthcare and autonomous systems. Awareness of the potential risks associated with XAI is needed as its adoption increases, driven in part by the need to enhance compliance to regulations. This survey provides a holistic perspective on the security and safety landscape surrounding XAI, categorizing research on adversarial attacks against XAI and the misuse of explainability to enhance attacks on AI systems, such as evasion and privacy breaches. Our contribution includes identifying current insecurities in XAI and outlining future research directions in adversarial XAI. This work serves as an accessible foundation and outlook to recognize potential research gaps and define future directions. It identifies data modalities, such as time-series or graph data, and XAI methods that have not been extensively investigated for vulnerabilities in current research.
Cite as

Elisabeth Pachl, Fabian Langer, Thora Markert, and Jeanette Miriam Lorenz. A View on Vulnerabilites: The Security Challenges of XAI (Academic Track). In Symposium on Scaling AI Assessments (SAIA 2024). Open Access Series in Informatics (OASIcs), Volume 126, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{pachl_et_al:OASIcs.SAIA.2024.12,
  author =	{Pachl, Elisabeth and Langer, Fabian and Markert, Thora and Lorenz, Jeanette Miriam},
  title =	{{A View on Vulnerabilites: The Security Challenges of XAI}},
  booktitle =	{Symposium on Scaling AI Assessments (SAIA 2024)},
  pages =	{12:1--12:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-357-7},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{126},
  editor =	{G\"{o}rge, Rebekka and Haedecke, Elena and Poretschkin, Maximilian and Schmitz, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SAIA.2024.12},
  URN =		{urn:nbn:de:0030-drops-227523},
  doi =		{10.4230/OASIcs.SAIA.2024.12},
  annote =	{Keywords: Explainability, XAI, Transparency, Adversarial Machine Learning, Security, Vulnerabilities}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.60
Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data

Authors: Hubert Wagner

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We focus on efficient computations of topological descriptors for voxel data. This type of data includes 2D greyscale images, 3D medical scans, but also higher-dimensional scalar fields arising from physical simulations. In recent years we have seen an increase in applications of topological methods for such data. However, computational issues remain an obstacle. We therefore propose a streaming scheme which simplifies large 3-dimensional voxel data - while provably retaining its persistent homology. We combine this scheme with an efficient boundary matrix reduction implementation, obtaining an end-to-end tool for persistent homology of large data. Computational experiments show its state-of-the-art performance. In particular, we are now able to robustly handle complex datasets with several billions voxels on a regular laptop. A software implementation called Cubicle is available as open-source: https://bitbucket.org/hubwag/cubicle.
Cite as

Hubert Wagner. Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{wagner:LIPIcs.SoCG.2023.60,
  author =	{Wagner, Hubert},
  title =	{{Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.60},
  URN =		{urn:nbn:de:0030-drops-179107},
  doi =		{10.4230/LIPIcs.SoCG.2023.60},
  annote =	{Keywords: Computational topology, topological data analysis, topological image analysis, persistent homology, persistence diagram, discrete Morse theory, algorithm engineering, implementation, voxel data, volume data, image data}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.64
GPU Computation of the Euler Characteristic Curve for Imaging Data

Authors: Fan Wang, Hubert Wagner, and Chao Chen

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Persistent homology is perhaps the most popular and useful tool offered by topological data analysis - with point-cloud data being the most common setup. Its older cousin, the Euler characteristic curve (ECC) is less expressive - but far easier to compute. It is particularly suitable for analyzing imaging data, and is commonly used in fields ranging from astrophysics to biomedical image analysis. These fields are embracing GPU computations to handle increasingly large datasets. We therefore propose an optimized GPU implementation of ECC computation for 2D and 3D grayscale images. The goal of this paper is twofold. First, we offer a practical tool, illustrating its performance with thorough experimentation - but also explain its inherent shortcomings. Second, this simple algorithm serves as a perfect backdrop for highlighting basic GPU programming techniques that make our implementation so efficient - and some common pitfalls we avoided. This is intended as a step towards a wider usage of GPU programming in computational geometry and topology software. We find this is particularly important as geometric and topological tools are used in conjunction with modern, GPU-accelerated machine learning frameworks.
Cite as

Fan Wang, Hubert Wagner, and Chao Chen. GPU Computation of the Euler Characteristic Curve for Imaging Data. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{wang_et_al:LIPIcs.SoCG.2022.64,
  author =	{Wang, Fan and Wagner, Hubert and Chen, Chao},
  title =	{{GPU Computation of the Euler Characteristic Curve for Imaging Data}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.64},
  URN =		{urn:nbn:de:0030-drops-160724},
  doi =		{10.4230/LIPIcs.SoCG.2022.64},
  annote =	{Keywords: topological data analysis, Euler characteristic, Euler characteristic curve, Betti curve, persistent homology, algorithms, parallel programming, algorithm engineering, GPU programming, imaging data}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.31
Topological Data Analysis in Information Space

Authors: Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.
Cite as

Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner. Topological Data Analysis in Information Space. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2019.31,
  author =	{Edelsbrunner, Herbert and Virk, \v{Z}iga and Wagner, Hubert},
  title =	{{Topological Data Analysis in Information Space}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.31},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.35
Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors: Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.
Cite as

Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2018.35,
  author =	{Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert},
  title =	{{Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.35},
  URN =		{urn:nbn:de:0030-drops-87487},
  doi =		{10.4230/LIPIcs.SoCG.2018.35},
  annote =	{Keywords: Bregman divergence, smallest enclosing spheres, Chernoff points, convexity, barycenter polytopes}
}
  • Refine by Type
  • 15 Document/PDF
  • 10 Document/HTML
  • 1 Artifact

  • Refine by Publication Year
  • 4 2026
  • 7 2025
  • 1 2023
  • 1 2022
  • 1 2019
  • Show More...

  • Refine by Author
  • 8 Wagner, Hubert
  • 3 Edelsbrunner, Herbert
  • 2 Arustamyan, Nickolas
  • 2 Bubenik, Peter
  • 2 Förster, Henry
  • Show More...

  • Refine by Series/Journal
  • 14 LIPIcs
  • 1 OASIcs

  • Refine by Classification
  • 7 Theory of computation → Computational geometry
  • 4 Mathematics of computing → Algebraic topology
  • 4 Mathematics of computing → Combinatorial algorithms
  • 2 Computing methodologies → Algebraic algorithms
  • 1 Computing methodologies → Linear algebra algorithms
  • Show More...

  • Refine by Keyword
  • 7 persistent homology
  • 2 Bregman divergence
  • 2 Computational topology
  • 2 Topological data analysis
  • 2 algorithm engineering
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact