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- W2108762162 abstract "We study a generalization of the k-median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P, our goal is to find a set C of size k such that the sum of errors D(P, C) = Σp∈P minc∈C{D(p, c)} is minimized. The main result in this paper can be stated as follows: There exists an O(n2k/e)O(1)) time (1 + e)-approximation algorithm for the k-median problem with respect to D, if the 1-median problem can be approximated within a factor of (1 + e) by taking a random sample of constant size and solving the 1-median problem on the sample exactly. Using this characterization, we obtain the first linear time (1 + e)-approximation algorithms for the k-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback-Leibler divergence (relative entropy), for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean k-median problem and the Euclidean k-means problem in a simplified manner. Our results are based on a new analysis of an algorithm from [20]." @default.
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- W2108762162 date "2008-01-20" @default.
- W2108762162 modified "2023-10-01" @default.
- W2108762162 title "Clustering for metric and non-metric distance measures" @default.
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