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TALG

2010

2010

We study a generalization of the k-median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P of size n, our goal is to find a set C of size k such that the sum of errors D(P, C) = pP mincC {D(p, c)} is minimized. The main result in this article can be stated as follows: There exists a (1 + )-approximation algorithm for the k-median problem with respect to D, if the 1-median problem can be approximated within a factor of (1 + ) by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithm requires time n2O(mklog(mk/ )) , where m is a constant that depends only on and D. Using this characterization, we obtain the first linear time (1 + )-approximation algorithms for the k-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback-Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman diver...

Related Content

Added |
21 May 2011 |

Updated |
21 May 2011 |

Type |
Journal |

Year |
2010 |

Where |
TALG |

Authors |
Marcel R. Ackermann, Johannes Blömer, Christian Sohler |

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