13 Search Results for "Sheehy, Donald R."

Document
DOI: 10.4230/LIPIcs.SoCG.2025.6
A Sparse Multicover Bifiltration of Linear Size

Authors: Ángel Javier Alonso

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

Abstract
The k-cover of a point cloud X of ℝ^d at radius r is the set of all those points within distance r of at least k points of X. By varying r and k we obtain a two-parameter filtration known as the multicover bifiltration. This bifiltration has received attention recently due to being choice-free and robust to outliers. However, it is hard to compute: the smallest known equivalent simplicial bifiltration has O(|X|^{d+1}) simplices. In this paper we introduce a (1+ε)-approximation of the multicover bifiltration of linear size O(|X|), for fixed d and ε. The methods also apply to the subdivision Rips bifiltration on metric spaces of bounded doubling dimension yielding analogous results.
Cite as

Ángel Javier Alonso. A Sparse Multicover Bifiltration of Linear Size. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alonso:LIPIcs.SoCG.2025.6,
  author =	{Alonso, \'{A}ngel Javier},
  title =	{{A Sparse Multicover Bifiltration of Linear Size}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{6:1--6:18},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-231587},
  doi =		{10.4230/LIPIcs.SoCG.2025.6},
  annote =	{Keywords: Multicover, Approximation, Sparsification, Multiparameter persistence}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.35
A Theory of Sub-Barcodes

Authors: Oliver A. Chubet, Kirk P. Gardner, and Donald R. Sheehy

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

Abstract
The primary tool in topological data analysis (TDA) is persistent homology, which involves computing a barcode - often from point-cloud or scalar field data - that serves as a topological signature for the underlying function. In this work, we introduce sub-barcodes and show how they arise naturally from factorizations of persistence module homomorphisms. We show that, as a partial order induced by factorizations, the relation of being a sub-barcode is strictly stronger than the rank invariant, and we apply sub-barcode theory to the problem of inferring information about the barcode of an unknown Lipschitz function from samples. The advantage of this approach is that it permits strong guarantees - with no noise - while requiring no sampling assumptions, and the resulting barcode is guaranteed to be a sub-barcode of every Lipschitz function that agrees with the data. We also present an algorithmic theory that allows for the efficient approximation of sub-barcodes using filtered Delaunay triangulations for Euclidean inputs.
Cite as

Oliver A. Chubet, Kirk P. Gardner, and Donald R. Sheehy. A Theory of Sub-Barcodes. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chubet_et_al:LIPIcs.SoCG.2025.35,
  author =	{Chubet, Oliver A. and Gardner, Kirk P. and Sheehy, Donald R.},
  title =	{{A Theory of Sub-Barcodes}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{35:1--35:16},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-231873},
  doi =		{10.4230/LIPIcs.SoCG.2025.35},
  annote =	{Keywords: Topology, Topological Data Analysis, Persistent Homology, Persistence Modules, Barcodes, Sub-barcodes, Factorizations, Lipschitz Extensions}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.64
Super-Polynomial Growth of the Generalized Persistence Diagram

Authors: Donghan Kim, Woojin Kim, and Wonjun Lee

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

Abstract
The Generalized Persistence Diagram (GPD) for multi-parameter persistence naturally extends the classical notion of persistence diagram for one-parameter persistence. However, unlike its classical counterpart, computing the GPD remains a significant challenge. The main hurdle is that, while the GPD is defined as the Möbius inversion of the Generalized Rank Invariant (GRI), computing the GRI is intractable due to the formidable size of its domain, i.e., the set of all connected and convex subsets in a finite grid in ℝ^d with d ≥ 2. This computational intractability suggests seeking alternative approaches to computing the GPD. In order to study the complexity associated to computing the GPD, it is useful to consider its classical one-parameter counterpart, where for a filtration of a simplicial complex with n simplices, its persistence diagram contains at most n points. This observation leads to the question: Given a d-parameter simplicial filtration, could the cardinality of its GPD (specifically, the support of the GPD) also be bounded by a polynomial in the number of simplices in the filtration? This is the case for d = 1, where we compute the persistence diagram directly at the simplicial filtration level. If this were also the case for d ≥ 2, it might be possible to compute the GPD directly and much more efficiently without relying on the GRI. We show that the answer to the question above is negative, demonstrating the inherent difficulty of computing the GPD. More specifically, we construct a sequence of d-parameter simplicial filtrations where the cardinalities of their GPDs are not bounded by any polynomial in the number of simplices. Furthermore, we show that several commonly used methods for constructing multi-parameter filtrations can give rise to such "wild" filtrations.
Cite as

Donghan Kim, Woojin Kim, and Wonjun Lee. Super-Polynomial Growth of the Generalized Persistence Diagram. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 64:1-64:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim_et_al:LIPIcs.SoCG.2025.64,
  author =	{Kim, Donghan and Kim, Woojin and Lee, Wonjun},
  title =	{{Super-Polynomial Growth of the Generalized Persistence Diagram}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{64:1--64:20},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-232162},
  doi =		{10.4230/LIPIcs.SoCG.2025.64},
  annote =	{Keywords: Persistent homology, M\"{o}bius inversion, Multiparameter persistence, Generalized persistence diagram, Generalized rank invariant}
}
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)

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@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
DOI: 10.4230/LIPIcs.SoCG.2025.10
Steinhaus Filtration and Stable Paths in the Mapper

Authors: Dustin L. Arendt, Matthew Broussard, Bala Krishnamoorthy, Nathaniel Saul, and Amber Thrall

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

Abstract
We define a new filtration called the Steinhaus filtration built from a single cover based on a generalized Steinhaus distance, a generalization of Jaccard distance. The homology persistence module of a Steinhaus filtration with infinitely many cover elements may not be q-tame, even when the covers are in a totally bounded space. While this may pose a challenge to derive stability results, we show that the Steinhaus filtration is stable when the cover is finite. We show that while the Čech and Steinhaus filtrations are not isomorphic in general, they are isomorphic for a finite point set in dimension one. Furthermore, the VR filtration completely determines the 1-skeleton of the Steinhaus filtration in arbitrary dimension. We then develop a language and theory for stable paths within the Steinhaus filtration. We demonstrate how the framework can be applied to several applications where a standard metric may not be defined but a cover is readily available. We introduce a new perspective for modeling recommendation system datasets. As an example, we look at a movies dataset and we find the stable paths identified in our framework represent a sequence of movies constituting a gentle transition and ordering from one genre to another. For explainable machine learning, we apply the Mapper algorithm for model induction by building a filtration from a single Mapper complex, and provide explanations in the form of stable paths between subpopulations. For illustration, we build a Mapper complex from a supervised machine learning model trained on the FashionMNIST dataset. Stable paths in the Steinhaus filtration provide improved explanations of relationships between subpopulations of images.
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Dustin L. Arendt, Matthew Broussard, Bala Krishnamoorthy, Nathaniel Saul, and Amber Thrall. Steinhaus Filtration and Stable Paths in the Mapper. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arendt_et_al:LIPIcs.SoCG.2025.10,
  author =	{Arendt, Dustin L. and Broussard, Matthew and Krishnamoorthy, Bala and Saul, Nathaniel and Thrall, Amber},
  title =	{{Steinhaus Filtration and Stable Paths in the Mapper}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{10:1--10:21},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-231625},
  doi =		{10.4230/LIPIcs.SoCG.2025.10},
  annote =	{Keywords: Cover and nerve, Jaccard distance, persistence stability, Mapper, recommender systems, explainable machine learning}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2023.64
Greedy Permutations and Finite Voronoi Diagrams (Media Exposition)

Authors: Oliver A. Chubet, Paul Macnichol, Parth Parikh, Donald R. Sheehy, and Siddharth S. Sheth

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

Abstract
We illustrate the computation of a greedy permutation using finite Voronoi diagrams. We describe the neighbor graph, which is a sparse graph data structure that facilitates efficient point location to insert a new Voronoi cell. This data structure is not dependent on a Euclidean metric space. The greedy permutation is computed in O(nlog Δ) time for low-dimensional data using this method [Sariel Har-Peled and Manor Mendel, 2006; Donald R. Sheehy, 2020].
Cite as

Oliver A. Chubet, Paul Macnichol, Parth Parikh, Donald R. Sheehy, and Siddharth S. Sheth. Greedy Permutations and Finite Voronoi Diagrams (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 64:1-64:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chubet_et_al:LIPIcs.SoCG.2023.64,
  author =	{Chubet, Oliver A. and Macnichol, Paul and Parikh, Parth and Sheehy, Donald R. and Sheth, Siddharth S.},
  title =	{{Greedy Permutations and Finite Voronoi Diagrams}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{64:1--64:5},
  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.2023.64},
  URN =		{urn:nbn:de:0030-drops-179146},
  doi =		{10.4230/LIPIcs.SoCG.2023.64},
  annote =	{Keywords: greedy permutation, Voronoi diagrams}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2023.65
The Sum of Squares in Polycubes (Media Exposition)

Authors: Donald R. Sheehy

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

Abstract
We give several ways to derive and express classic summation problems in terms of polycubes. We visualize them with 3D printed models. The video is here: http://go.ncsu.edu/sum_of_squares.
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Donald R. Sheehy. The Sum of Squares in Polycubes (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 65:1-65:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{sheehy:LIPIcs.SoCG.2023.65,
  author =	{Sheehy, Donald R.},
  title =	{{The Sum of Squares in Polycubes}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{65:1--65:6},
  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.2023.65},
  URN =		{urn:nbn:de:0030-drops-179152},
  doi =		{10.4230/LIPIcs.SoCG.2023.65},
  annote =	{Keywords: Archimedes, polycubes, sum of squares}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.60
Nearly-Doubling Spaces of Persistence Diagrams

Authors: Donald R. Sheehy and Siddharth S. Sheth

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

Abstract
The space of persistence diagrams under bottleneck distance is known to have infinite doubling dimension. Because many metric search algorithms and data structures have bounds that depend on the dimension of the search space, the high-dimensionality makes it difficult to analyze and compare asymptotic running times of metric search algorithms on this space. We introduce the notion of nearly-doubling metrics, those that are Gromov-Hausdorff close to metric spaces of bounded doubling dimension and prove that bounded k-point persistence diagrams are nearly-doubling. This allows us to prove that in some ways, persistence diagrams can be expected to behave like a doubling metric space. We prove our results in great generality, studying a large class of quotient metrics (of which the persistence plane is just one example). We also prove bounds on the dimension of the k-point bottleneck space over such metrics. The notion of being nearly-doubling in this Gromov-Hausdorff sense is likely of more general interest. Some algorithms that have a dependence on the dimension can be analyzed in terms of the dimension of the nearby metric rather than that of the metric itself. We give a specific example of this phenomenon by analyzing an algorithm to compute metric nets, a useful operation on persistence diagrams.
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Donald R. Sheehy and Siddharth S. Sheth. Nearly-Doubling Spaces of Persistence Diagrams. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 60:1-60:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{sheehy_et_al:LIPIcs.SoCG.2022.60,
  author =	{Sheehy, Donald R. and Sheth, Siddharth S.},
  title =	{{Nearly-Doubling Spaces of Persistence Diagrams}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{60:1--60:15},
  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.2022.60},
  URN =		{urn:nbn:de:0030-drops-160686},
  doi =		{10.4230/LIPIcs.SoCG.2022.60},
  annote =	{Keywords: Topological Data Analysis, Persistence Diagrams, Gromov-Hausdorff Distance}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.57
Sketching Persistence Diagrams

Authors: Donald R. Sheehy and Siddharth Sheth

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
Given a persistence diagram with n points, we give an algorithm that produces a sequence of n persistence diagrams converging in bottleneck distance to the input diagram, the ith of which has i distinct (weighted) points and is a 2-approximation to the closest persistence diagram with that many distinct points. For each approximation, we precompute the optimal matching between the ith and the (i+1)st. Perhaps surprisingly, the entire sequence of diagrams as well as the sequence of matchings can be represented in O(n) space. The main approach is to use a variation of the greedy permutation of the persistence diagram to give good Hausdorff approximations and assign weights to these subsets. We give a new algorithm to efficiently compute this permutation, despite the high implicit dimension of points in a persistence diagram due to the effect of the diagonal. The sketches are also structured to permit fast (linear time) approximations to the Hausdorff distance between diagrams - a lower bound on the bottleneck distance. For approximating the bottleneck distance, sketches can also be used to compute a linear-size neighborhood graph directly, obviating the need for geometric data structures used in state-of-the-art methods for bottleneck computation.
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Donald R. Sheehy and Siddharth Sheth. Sketching Persistence Diagrams. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sheehy_et_al:LIPIcs.SoCG.2021.57,
  author =	{Sheehy, Donald R. and Sheth, Siddharth},
  title =	{{Sketching Persistence Diagrams}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.57},
  URN =		{urn:nbn:de:0030-drops-138569},
  doi =		{10.4230/LIPIcs.SoCG.2021.57},
  annote =	{Keywords: Bottleneck Distance, Persistent Homology, Approximate Persistence Diagrams}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.58
A Sparse Delaunay Filtration

Authors: Donald R. Sheehy

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We show how a filtration of Delaunay complexes can be used to approximate the persistence diagram of the distance to a point set in ℝ^d. Whereas the full Delaunay complex can be used to compute this persistence diagram exactly, it may have size O(n^⌈d/2⌉). In contrast, our construction uses only O(n) simplices. The central idea is to connect Delaunay complexes on progressively denser subsamples by considering the flips in an incremental construction as simplices in d+1 dimensions. This approach leads to a very simple and straightforward proof of correctness in geometric terms, because the final filtration is dual to a (d+1)-dimensional Voronoi construction similar to the standard Delaunay filtration. We also, show how this complex can be efficiently constructed.
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Donald R. Sheehy. A Sparse Delaunay Filtration. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 58:1-58:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sheehy:LIPIcs.SoCG.2021.58,
  author =	{Sheehy, Donald R.},
  title =	{{A Sparse Delaunay Filtration}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{58:1--58:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.58},
  URN =		{urn:nbn:de:0030-drops-138579},
  doi =		{10.4230/LIPIcs.SoCG.2021.58},
  annote =	{Keywords: Delaunay Triangulation, Persistent Homology, Sparse Filtrations}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.64
Interactive Geometric Algorithm Visualization in a Browser

Authors: Kirk Gardner, Lynn Asselin, and Donald Sheehy

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
We present an online, interactive tool for writing and presenting interactive geometry demos suitable for classroom demonstrations. Code for the demonstrations is written in JavaScript using p5.js, a JavaScript library based on Processing.
Cite as

Kirk Gardner, Lynn Asselin, and Donald Sheehy. Interactive Geometric Algorithm Visualization in a Browser. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 64:1-64:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{gardner_et_al:LIPIcs.SoCG.2016.64,
  author =	{Gardner, Kirk and Asselin, Lynn and Sheehy, Donald},
  title =	{{Interactive Geometric Algorithm Visualization in a Browser}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{64:1--64:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.64},
  URN =		{urn:nbn:de:0030-drops-59563},
  doi =		{10.4230/LIPIcs.SoCG.2016.64},
  annote =	{Keywords: Computational Geometry, Processing, JavaScript, Visualisation, Incremental Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.69
Exploring Circle Packing Algorithms

Authors: Kevin Pratt, Connor Riley, and Donald Sheehy

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
We present an interactive tool for visualizing and experimenting with different circle packing algorithms.
Cite as

Kevin Pratt, Connor Riley, and Donald Sheehy. Exploring Circle Packing Algorithms. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 69:1-69:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{pratt_et_al:LIPIcs.SoCG.2016.69,
  author =	{Pratt, Kevin and Riley, Connor and Sheehy, Donald},
  title =	{{Exploring Circle Packing Algorithms}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{69:1--69:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.69},
  URN =		{urn:nbn:de:0030-drops-59616},
  doi =		{10.4230/LIPIcs.SoCG.2016.69},
  annote =	{Keywords: Computational Geometry, Processing, Javascript, Visualization, Incremental Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.23
Visualizing Sparse Filtrations

Authors: Nicholas J. Cavanna, Mahmoodreza Jahanseir, and Donald R. Sheehy

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
Over the last few years, there have been several approaches to building sparser complexes that still give good approximations to the persistent homology. In this video, we have illustrated a geometric perspective on sparse filtrations that leads to simpler proofs, more general theorems, and a more visual explanation. We hope that as these techniques become easier to understand, they will also become easier to use.
Cite as

Nicholas J. Cavanna, Mahmoodreza Jahanseir, and Donald R. Sheehy. Visualizing Sparse Filtrations. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 23-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{cavanna_et_al:LIPIcs.SOCG.2015.23,
  author =	{Cavanna, Nicholas J. and Jahanseir, Mahmoodreza and Sheehy, Donald R.},
  title =	{{Visualizing Sparse Filtrations}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{23--25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.23},
  URN =		{urn:nbn:de:0030-drops-50893},
  doi =		{10.4230/LIPIcs.SOCG.2015.23},
  annote =	{Keywords: Topological Data Analysis, Simplicial Complexes, Persistent Homology}
}
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