How fast is the k-means method?

Sariel Har-Peled, Bardia Sadri

Research output: Contribution to journalArticlepeer-review


We present polynomial upper and lower bounds on the number of iterations performed by the k-means method (a.k.a. Lloyd's method) for k-means clustering. Our upper bounds are polynomial in the number of points, number of clusters, and the spread of the point set. We also present a lower bound, showing that in the worst case the k-means heuristic needs to perform Ω(n) iterations, for n points on the real line and two centers. Surprisingly, the spread of the point set in this construction is polynomial. This is the first construction showing that the k-means heuristic requires more than a polylogarithmic number of iterations. Furthermore, we present two alternative algorithms, with guaranteed performance, which are simple variants of the k-means method. Results of our experimental studies on these algorithms are also presented.

Original languageEnglish (US)
Pages (from-to)185-202
Number of pages18
JournalAlgorithmica (New York)
Issue number3
StatePublished - Jan 2005


  • Classification
  • Clustering
  • K-Means method

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


Dive into the research topics of 'How fast is the k-means method?'. Together they form a unique fingerprint.

Cite this