3 Search Results for "Jung, Attila"

Document
DOI: 10.4230/LIPIcs.SoCG.2025.61
k-Dimensional Transversals for Fat Convex Sets

Authors: Attila Jung and Dömötör Pálvölgyi

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

Abstract
We prove a fractional Helly theorem for k-flats intersecting fat convex sets. A family ℱ of sets is said to be ρ-fat if every set in the family contains a ball and is contained in a ball such that the ratio of the radii of these balls is bounded by ρ. We prove that for every dimension d and positive reals ρ and α there exists a positive β = β(d,ρ, α) such that if ℱ is a finite family of ρ-fat convex sets in ℝ^d and an α-fraction of the (k+2)-size subfamilies from ℱ can be hit by a k-flat, then there is a k-flat that intersects at least a β-fraction of the sets of ℱ. We prove spherical and colorful variants of the above results and prove a (p,k+2)-theorem for k-flats intersecting balls.
Cite as

Attila Jung and Dömötör Pálvölgyi. k-Dimensional Transversals for Fat Convex Sets. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jung_et_al:LIPIcs.SoCG.2025.61,
  author =	{Jung, Attila and P\'{a}lv\"{o}lgyi, D\"{o}m\"{o}t\"{o}r},
  title =	{{k-Dimensional Transversals for Fat Convex Sets}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{61:1--61:12},
  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.2025.61},
  URN =		{urn:nbn:de:0030-drops-232136},
  doi =		{10.4230/LIPIcs.SoCG.2025.61},
  annote =	{Keywords: discrete geometry, transversals, Helly, hypergraphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.71
Banana Trees for the Persistence in Time Series Experimentally

Authors: Lara Ost, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner

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

Abstract
In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.
Cite as

Lara Ost, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner. Banana Trees for the Persistence in Time Series Experimentally. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 71:1-71:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ost_et_al:LIPIcs.SoCG.2025.71,
  author =	{Ost, Lara and Cultrera di Montesano, Sebastiano and Edelsbrunner, Herbert},
  title =	{{Banana Trees for the Persistence in Time Series Experimentally}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{71:1--71:13},
  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.2025.71},
  URN =		{urn:nbn:de:0030-drops-232237},
  doi =		{10.4230/LIPIcs.SoCG.2025.71},
  annote =	{Keywords: persistent homology, time series, data structures, computational experiments}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.8
On Helly Numbers of Exponential Lattices

Authors: Gergely Ambrus, Martin Balko, Nóra Frankl, Attila Jung, and Márton Naszódi

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

Abstract
Given a set S ⊆ ℝ², define the Helly number of S, denoted by H(S), as the smallest positive integer N, if it exists, for which the following statement is true: for any finite family ℱ of convex sets in ℝ² such that the intersection of any N or fewer members of ℱ contains at least one point of S, there is a point of S common to all members of ℱ. We prove that the Helly numbers of exponential lattices {αⁿ : n ∈ ℕ₀}² are finite for every α > 1 and we determine their exact values in some instances. In particular, we obtain H({2ⁿ : n ∈ ℕ₀}²) = 5, solving a problem posed by Dillon (2021). For real numbers α, β > 1, we also fully characterize exponential lattices L(α,β) = {αⁿ : n ∈ ℕ₀} × {βⁿ : n ∈ ℕ₀} with finite Helly numbers by showing that H(L(α,β)) is finite if and only if log_α(β) is rational.
Cite as

Gergely Ambrus, Martin Balko, Nóra Frankl, Attila Jung, and Márton Naszódi. On Helly Numbers of Exponential Lattices. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ambrus_et_al:LIPIcs.SoCG.2023.8,
  author =	{Ambrus, Gergely and Balko, Martin and Frankl, N\'{o}ra and Jung, Attila and Nasz\'{o}di, M\'{a}rton},
  title =	{{On Helly Numbers of Exponential Lattices}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{8:1--8:16},
  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.2023.8},
  URN =		{urn:nbn:de:0030-drops-178584},
  doi =		{10.4230/LIPIcs.SoCG.2023.8},
  annote =	{Keywords: Helly numbers, exponential lattices, Diophantine approximation}
}
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