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.ICALP.2016.19
URN: urn:nbn:de:0030-drops-63401
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6340/
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Cohen-Addad, Vincent ; Schwiegelshohn, Chris ; Sohler, Christian

Diameter and k-Center in Sliding Windows

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LIPIcs-ICALP-2016-19.pdf (0.5 MB)

Abstract

In this paper we develop streaming algorithms for the diameter problem and the k-center clustering problem in the sliding window model. In this model we are interested in maintaining a solution for the N most recent points of the stream. In the diameter problem we would like to maintain two points whose distance approximates the diameter of the point set in the window. Our algorithm computes a (3 + epsilon)-approximation and uses O(1/epsilon*ln(alpha)) memory cells, where alpha is the ratio of the largest and smallest distance and is assumed to be known in advance. We also prove that under reasonable assumptions obtaining a (3 - epsilon)-approximation requires Omega(N1/3) space.

For the k-center problem, where the goal is to find k centers that minimize the maximum distance of a point to its nearest center, we obtain a (6 + epsilon)-approximation using O(k/epsilon*ln(alpha)) memory cells and a (4 + epsilon)-approximation for the special case k = 2. We also prove that any algorithm for the 2-center problem that achieves an approximation ratio of less than 4 requires Omega(N^{1/3}) space.

BibTeX - Entry

@InProceedings{cohenaddad_et_al:LIPIcs:2016:6340,
  author =	{Vincent Cohen-Addad and Chris Schwiegelshohn and Christian Sohler},
  title =	{{Diameter and k-Center in Sliding Windows}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6340},
  URN =		{urn:nbn:de:0030-drops-63401},
  doi =		{10.4230/LIPIcs.ICALP.2016.19},
  annote =	{Keywords: Streaming, k-Center, Diameter, Sliding Windows}
}

Keywords: Streaming, k-Center, Diameter, Sliding Windows
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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