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.SWAT.2020.8
URN: urn:nbn:de:0030-drops-122551
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12255/
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Backurs, Arturs ; Har-Peled, Sariel

Submodular Clustering in Low Dimensions

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LIPIcs-SWAT-2020-8.pdf (0.5 MB)


Abstract

We study a clustering problem where the goal is to maximize the coverage of the input points by k chosen centers. Specifically, given a set of n points P ⊆ ℝ^d, the goal is to pick k centers C ⊆ ℝ^d that maximize the service ∑_{p∈P}φ(𝖽(p,C)) to the points P, where 𝖽(p,C) is the distance of p to its nearest center in C, and φ is a non-increasing service function φ: ℝ+ → ℝ+. This includes problems of placing k base stations as to maximize the total bandwidth to the clients - indeed, the closer the client is to its nearest base station, the more data it can send/receive, and the target is to place k base stations so that the total bandwidth is maximized. We provide an n^{ε^-O(d)} time algorithm for this problem that achieves a (1-ε)-approximation. Notably, the runtime does not depend on the parameter k and it works for an arbitrary non-increasing service function φ: ℝ+ → ℝ+.

BibTeX - Entry

@InProceedings{backurs_et_al:LIPIcs:2020:12255,
  author =	{Arturs Backurs and Sariel Har-Peled},
  title =	{{Submodular Clustering in Low Dimensions}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Susanne Albers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12255},
  URN =		{urn:nbn:de:0030-drops-122551},
  doi =		{10.4230/LIPIcs.SWAT.2020.8},
  annote =	{Keywords: clustering, covering, PTAS}
}

Keywords: clustering, covering, PTAS
Collection: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Issue Date: 2020
Date of publication: 12.06.2020


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