Sciweavers

Share
FOCS
2010
IEEE

Stability Yields a PTAS for k-Median and k-Means Clustering

8 years 11 months ago
Stability Yields a PTAS for k-Median and k-Means Clustering
We consider k-median clustering in finite metric spaces and k-means clustering in Euclidean spaces, in the setting where k is part of the input (not a constant). For the k-means problem, Ostrovsky et al. [18] show that if the optimal (k-1)-means clustering of the input is more expensive than the optimal k-means clustering by a factor of 1/2 , then one can achieve a (1 + f())-approximation to the k-means optimal in time polynomial in n and k by using a variant of Lloyd's algorithm. In this work we substantially improve this approximation guarantee. We show that given only the condition that the (k-1)-means optimal is more expensive than the k-means optimal by a factor 1+ for some constant > 0, we can obtain a PTAS. In particular, under this assumption, for any > 0 we achieve a (1 + )-approximation to the k-means optimal in time polynomial in n and k, and exponential in 1/ and 1/. We thus decouple the strength of the assumption from the quality of the approximation ratio. We...
Pranjal Awasthi, Avrim Blum, Or Sheffet
Added 11 Feb 2011
Updated 11 Feb 2011
Type Journal
Year 2010
Where FOCS
Authors Pranjal Awasthi, Avrim Blum, Or Sheffet
Comments (0)
books