License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.9
URN: urn:nbn:de:0030-drops-133530
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Gudmundsson, Joachim ; Sha, Yuan ; Wong, Sampson

Approximating the Packedness of Polygonal Curves

LIPIcs-ISAAC-2020-9.pdf (0.6 MB)


In 2012 Driemel et al. [Anne Driemel et al., 2012] introduced the concept of c-packed curves as a realistic input model. In the case when c is a constant they gave a near linear time (1+ε)-approximation algorithm for computing the Fréchet distance between two c-packed polygonal curves. Since then a number of papers have used the model.
In this paper we consider the problem of computing the smallest c for which a given polygonal curve in ℝ^d is c-packed. We present two approximation algorithms. The first algorithm is a 2-approximation algorithm and runs in O(dn² log n) time. In the case d = 2 we develop a faster algorithm that returns a (6+ε)-approximation and runs in O((n/ε³)^{4/3} polylog (n/ε))) time.
We also implemented the first algorithm and computed the approximate packedness-value for 16 sets of real-world trajectories. The experiments indicate that the notion of c-packedness is a useful realistic input model for many curves and trajectories.

BibTeX - Entry

  author =	{Joachim Gudmundsson and Yuan Sha and Sampson Wong},
  title =	{{Approximating the Packedness of Polygonal Curves}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-133530},
  doi =		{10.4230/LIPIcs.ISAAC.2020.9},
  annote =	{Keywords: Computational geometry, trajectories, realistic input models}

Keywords: Computational geometry, trajectories, realistic input models
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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