License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2016.78
URN: urn:nbn:de:0030-drops-64191
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6419/
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Roughgarden, Tim ; Wang, Joshua R.

The Complexity of the k-means Method

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LIPIcs-ESA-2016-78.pdf (0.5 MB)

Abstract

The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on the complexity of the simplex method for linear programming.

BibTeX - Entry

@InProceedings{roughgarden_et_al:LIPIcs:2016:6419,
  author =	{Tim Roughgarden and Joshua R. Wang},
  title =	{{The Complexity of the k-means Method}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{78:1--78:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6419},
  URN =		{urn:nbn:de:0030-drops-64191},
  doi =		{10.4230/LIPIcs.ESA.2016.78},
  annote =	{Keywords: k-means, PSPACE-complete}
}

Keywords: k-means, PSPACE-complete
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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