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ICALP

2005

Springer

2005

Springer

Abstract. We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2(k/ε)O(1) dn) time (1 + ε)-approximation algorithms for these problems. These are the ﬁrst algorithms for these problems linear in the size of the input (nd for n points in d dimensions), independent of dimensions in the exponent, assuming k and ε to be ﬁxed. A key ingredient of the k-median result is a (1 + ε)-approximation algorithm for the 1-median problem which has running time O(2(1/ε)O(1) d). The previous best known algorithm for this problem had linear running time.

Related Content

Added |
27 Jun 2010 |

Updated |
27 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
ICALP |

Authors |
Amit Kumar, Yogish Sabharwal, Sandeep Sen |

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