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The Complexity of the k-means Method

Authors Tim Roughgarden, Joshua R. Wang

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Tim Roughgarden
Joshua R. Wang

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Tim Roughgarden and Joshua R. Wang. The Complexity of the k-means Method. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ESA.2016.78

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.

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Keywords
  • k-means
  • PSPACE-complete

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