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Author Kumar, Amit ♦ Sabharwal, Yogish ♦ Sen, Sandeep
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2010
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Clustering ♦ Approximation ♦ K-means ♦ K-medians
Abstract 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 $\textit{k}-means,$ $\textit{k}-median$ and discrete $\textit{k}-means$ problems that yield (1+ϵ) approximations with probability ≥ 1/2 and running times of $O(2^{(k/ϵ)^{O(1)}}$ $\textit{dn}).$ These are the first algorithms for these problems whose running times are linear in the size of the input $(\textit{nd}$ for $\textit{n}$ points in $\textit{d}$ dimensions) assuming $\textit{k}$ and ϵ are fixed. Our method is general enough to be applicable to clustering problems satisfying certain simple properties and is likely to have further applications.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2010-02-08
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 57
Issue Number 2
Page Count 32
Starting Page 1
Ending Page 32


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Source: ACM Digital Library