License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.10
URN: urn:nbn:de:0030-drops-172950
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17295/
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Fox, Kyle ; Huang, Hongyao ; Raichel, Benjamin

Clustering with Faulty Centers

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LIPIcs-ISAAC-2022-10.pdf (0.6 MB)

Abstract

In this paper we introduce and formally study the problem of k-clustering with faulty centers. Specifically, we study the faulty versions of k-center, k-median, and k-means clustering, where centers have some probability of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters k, d, and ε, that (1+ε)-approximate the minimum expected cost solutions for points in d dimensional Euclidean space. For Faulty k-center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have a small dependence on n. Specifically, our Faulty k-center algorithms have only linear dependence on n, while for our algorithms for Faulty k-median and Faulty k-means the dependence is still only n^(1 + o(1)).

BibTeX - Entry

@InProceedings{fox_et_al:LIPIcs.ISAAC.2022.10,
  author =	{Fox, Kyle and Huang, Hongyao and Raichel, Benjamin},
  title =	{{Clustering with Faulty Centers}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17295},
  URN =		{urn:nbn:de:0030-drops-172950},
  doi =		{10.4230/LIPIcs.ISAAC.2022.10},
  annote =	{Keywords: clustering, approximation, probabilistic input, uncertain input}
}

Keywords: clustering, approximation, probabilistic input, uncertain input
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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