3 Search Results for "Chun, Jinhee"

Document
DOI: 10.4230/LIPIcs.ESA.2025.21
A Unified FPT Framework for Crossing Number Problems

Authors: Éric Colin de Verdière and Petr Hliněný

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework that smoothly captures many generalized crossing number problems, and that yields fixed-parameter tractable (FPT) algorithms for them not only in the plane but also on surfaces. Our framework takes the following form. We fix a surface S, an integer r, and a map κ from the set of topological drawings of graphs in S to ℤ_+ ∪ {∞}, satisfying some natural monotonicity conditions, but essentially describing the allowed drawings and how we want to count the crossings in them. Then deciding whether an input graph G has an allowed drawing D on S with κ(D) ≤ r can be done in time quadratic in the size of G (and exponential in other parameters). More generally, we may take as input an edge-colored graph, and distinguish crossings by the colors of the involved edges; and we may allow to perform a bounded number of edge removals and vertex splits to G before drawing it. The proof is a reduction to the embeddability of a graph on a two-dimensional simplicial complex. This framework implies, in a unified way, quadratic FPT algorithms for many topological crossing number variants established in the graph drawing community. Some of these variants already had previously published FPT algorithms, mostly relying on Courcelle’s metatheorem, but for many of those, we obtain an algorithm with a better runtime. Moreover, our framework extends, at no cost, to these crossing number variants in any fixed surface.
Cite as

Éric Colin de Verdière and Petr Hliněný. A Unified FPT Framework for Crossing Number Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{colindeverdiere_et_al:LIPIcs.ESA.2025.21,
  author =	{Colin de Verdi\`{e}re, \'{E}ric and Hlin\v{e}n\'{y}, Petr},
  title =	{{A Unified FPT Framework for Crossing Number Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.21},
  URN =		{urn:nbn:de:0030-drops-244897},
  doi =		{10.4230/LIPIcs.ESA.2025.21},
  annote =	{Keywords: computational geometry, fixed-parameter tractability, graph drawing, graph embedding, crossing number, two-dimensional simplicial complex, surface}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.32
Consistent Digital Curved Rays and Pseudoline Arrangements

Authors: Jinhee Chun, Kenya Kikuchi, and Takeshi Tokuyama

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Representing a family of geometric objects in the digital world where each object is represented by a set of pixels is a basic problem in graphics and computational geometry. One important criterion is the consistency, where the intersection pattern of the objects should be consistent with axioms of the Euclidean geometry, e.g., the intersection of two lines should be a single connected component. Previously, the set of linear rays and segments has been considered. In this paper, we extended this theory to families of curved rays going through the origin. We further consider some psudoline arrangements obtained as unions of such families of rays.
Cite as

Jinhee Chun, Kenya Kikuchi, and Takeshi Tokuyama. Consistent Digital Curved Rays and Pseudoline Arrangements. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{chun_et_al:LIPIcs.ESA.2019.32,
  author =	{Chun, Jinhee and Kikuchi, Kenya and Tokuyama, Takeshi},
  title =	{{Consistent Digital Curved Rays and Pseudoline Arrangements}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.32},
  URN =		{urn:nbn:de:0030-drops-111538},
  doi =		{10.4230/LIPIcs.ESA.2019.32},
  annote =	{Keywords: Computational Geometry, Digital Geometry, Spanning Tree, Graph Drawing}
}
Document
Multimedia Contribution
DOI: 10.4230/LIPIcs.SoCG.2017.64
Folding Free-Space Diagrams: Computing the Fréchet Distance between 1-Dimensional Curves (Multimedia Contribution)

Authors: Kevin Buchin, Jinhee Chun, Maarten Löffler, Aleksandar Markovic, Wouter Meulemans, Yoshio Okamoto, and Taichi Shiitada

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
By folding the free-space diagram for efficient preprocessing, we show that the Frechet distance between 1D curves can be computed in O(nk log n) time, assuming one curve has ply k.
Cite as

Kevin Buchin, Jinhee Chun, Maarten Löffler, Aleksandar Markovic, Wouter Meulemans, Yoshio Okamoto, and Taichi Shiitada. Folding Free-Space Diagrams: Computing the Fréchet Distance between 1-Dimensional Curves (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 64:1-64:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{buchin_et_al:LIPIcs.SoCG.2017.64,
  author =	{Buchin, Kevin and Chun, Jinhee and L\"{o}ffler, Maarten and Markovic, Aleksandar and Meulemans, Wouter and Okamoto, Yoshio and Shiitada, Taichi},
  title =	{{Folding Free-Space Diagrams: Computing the Fr\'{e}chet Distance between 1-Dimensional Curves}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{64:1--64:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.64},
  URN =		{urn:nbn:de:0030-drops-72417},
  doi =		{10.4230/LIPIcs.SoCG.2017.64},
  annote =	{Keywords: Frechet distance, ply, k-packed curves}
}
  • Refine by Type
  • 3 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2019
  • 1 2017

  • Refine by Author
  • 2 Chun, Jinhee
  • 1 Buchin, Kevin
  • 1 Colin de Verdière, Éric
  • 1 Hliněný, Petr
  • 1 Kikuchi, Kenya
  • Show More...

  • Refine by Series/Journal
  • 3 LIPIcs

  • Refine by Classification
  • 2 Theory of computation → Computational geometry
  • 1 Mathematics of computing → Graph theory
  • 1 Theory of computation → Fixed parameter tractability

  • Refine by Keyword
  • 1 Computational Geometry
  • 1 Digital Geometry
  • 1 Frechet distance
  • 1 Graph Drawing
  • 1 Spanning Tree
  • 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