Approximation schemes for clustering problems

We present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions. More specifically, our approach leads to simple randomized algorithms for the k-means, k-median and discrete k-means problems that yield (1 + ) approximations with probability 1/2 and running times of O(2(k/)O(1) dn). These are the first algorithms for these problems whose running times are linear in the size of the input (nd for n points in d dimensions) assuming k and are fixed. Our method is general enough to be applicable to clustering problems satisfying certain simple properties and is likely to have further applications.

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Wenceslas Fernandez de la Vega, Marek Karpinski, Claire Kenyon, Yuval Rabani
• Keywords: Algorithms, Certain Simple Properties, Discrete K-means Problems, Geometric Clustering Problems, STOC 2003