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.SoCG.2020.58
URN: urn:nbn:de:0030-drops-122161
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12216/
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Nath, Abhinandan ; Taylor, Erin

k-Median Clustering Under Discrete Fréchet and Hausdorff Distances

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Abstract

We give the first near-linear time (1+ε)-approximation algorithm for k-median clustering of polygonal trajectories under the discrete Fréchet distance, and the first polynomial time (1+ε)-approximation algorithm for k-median clustering of finite point sets under the Hausdorff distance, provided the cluster centers, ambient dimension, and k are bounded by a constant. The main technique is a general framework for solving clustering problems where the cluster centers are restricted to come from a simpler metric space. We precisely characterize conditions on the simpler metric space of the cluster centers that allow faster (1+ε)-approximations for the k-median problem. We also show that the k-median problem under Hausdorff distance is NP-Hard.

BibTeX - Entry

@InProceedings{nath_et_al:LIPIcs:2020:12216,
  author =	{Abhinandan Nath and Erin Taylor},
  title =	{{k-Median Clustering Under Discrete Fr{\'e}chet and Hausdorff Distances}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12216},
  URN =		{urn:nbn:de:0030-drops-122161},
  doi =		{10.4230/LIPIcs.SoCG.2020.58},
  annote =	{Keywords: Clustering, k-median, trajectories, point sets, discrete Fr{\'e}chet distance, Hausdorff distance}
}

Keywords: Clustering, k-median, trajectories, point sets, discrete Fréchet distance, Hausdorff distance
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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