How slow is the k-means method?

@inproceedings{Arthur2006HowSI,
  title={How slow is the k-means method?},
  author={David Arthur and Sergei Vassilvitskii},
  booktitle={SCG '06},
  year={2006}
}
The <b>k-means</b> method is an old but popular clustering algorithm known for its observed speed and its simplicity. Until recently, however, no meaningful theoretical bounds were known on its running time. In this paper, we demonstrate that the worst-case running time of <b>k-means</b> is <i>superpolynomial</i> by improving the best known lower bound from Ω<i>(n)</i> iterations to 2<sup>Ω(√<i>n</i>)</sup>. 
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