1 Search Results for "Alves Akitaya, Hugo"

Document
DOI: 10.4230/LIPIcs.ISAAC.2019.50
The k-Fréchet Distance: How to Walk Your Dog While Teleporting

Authors: Hugo Alves Akitaya, Maike Buchin, Leonie Ryvkin, and Jérôme Urhausen

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We introduce a new distance measure for comparing polygonal chains: the k-Fréchet distance. As the name implies, it is closely related to the well-studied Fréchet distance but detects similarities between curves that resemble each other only piecewise. The parameter k denotes the number of subcurves into which we divide the input curves (thus we allow up to k-1 "teleports" on each input curve). The k-Fréchet distance provides a nice transition between (weak) Fréchet distance and Hausdorff distance. However, we show that deciding this distance measure turns out to be NP-hard, which is interesting since both (weak) Fréchet and Hausdorff distance are computable in polynomial time. Nevertheless, we give several possibilities to deal with the hardness of the k-Fréchet distance: besides a short exponential-time algorithm for the general case, we give a polynomial-time algorithm for k=2, i.e., we ask that we subdivide our input curves into two subcurves each. We can also approximate the optimal k by factor 2. We then present a more intricate FPT algorithm using parameters k (the number of allowed subcurves) and z (the number of segments of one curve that intersect the epsilon-neighborhood of a point on the other curve).
Cite as

Hugo Alves Akitaya, Maike Buchin, Leonie Ryvkin, and Jérôme Urhausen. The k-Fréchet Distance: How to Walk Your Dog While Teleporting. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{alvesakitaya_et_al:LIPIcs.ISAAC.2019.50,
  author =	{Alves Akitaya, Hugo and Buchin, Maike and Ryvkin, Leonie and Urhausen, J\'{e}r\^{o}me},
  title =	{{The k-Fr\'{e}chet Distance: How to Walk Your Dog While Teleporting}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.50},
  URN =		{urn:nbn:de:0030-drops-115462},
  doi =		{10.4230/LIPIcs.ISAAC.2019.50},
  annote =	{Keywords: Measures, Fr\'{e}chet distance, Hardness, FPT}
}
  • Refine by Author
  • 1 Alves Akitaya, Hugo
  • 1 Buchin, Maike
  • 1 Ryvkin, Leonie
  • 1 Urhausen, Jérôme

  • Refine by Classification
  • 1 Theory of computation → Computational geometry
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Fixed parameter tractability

  • Refine by Keyword
  • 1 FPT
  • 1 Fréchet distance
  • 1 Hardness
  • 1 Measures

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2019

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact