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ISAAC

2005

Springer

2005

Springer

In this paper we study the k-means clustering problem. It is well-known that the general version of this problem is NP-hard. Numerous approximation algorithms have been proposed for this problem. In this paper, we proposed three constant approximation algorithms for k-means clustering. The ﬁrst algorithm runs in time O((k )k nd), where k is the number of clusters, n is the size of input points, d is dimension of attributes. The second algorithm runs in time O(k3 n2 log n). This is the ﬁrst algorithm for k-means clustering that runs in time polynomial in n, k and d. The run time of the third algorithm O(k5 log3 kd) ¡ is independent of n. Though an algorithm whose run time is independent of n is known for the k-median problem, ours is the ﬁrst such algorithm for the k-means problem.

Related Content

Added |
27 Jun 2010 |

Updated |
27 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
ISAAC |

Authors |
Mingjun Song, Sanguthevar Rajasekaran |

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