Improved analysis of D2-sampling based PTAS for k-means and other clustering problems

We give an improved analysis of the simple D2-sampling based PTAS for the k-means clustering problem given by Jaiswal et al. [3]. The improvement on the running time is from O(nd⋅2O˜(k2/ϵ)) to O(nd⋅2O˜(k/ϵ)). •We give improved analysis of the Jaiswal–Kumar–Sen algorithm [3].•We get a better running...

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Bibliographic Details
Published inInformation processing letters Vol. 115; no. 2; pp. 100 - 103
Main Authors Jaiswal, Ragesh, Kumar, Mehul, Yadav, Pulkit
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2015
Subjects
[formula omitted]-sampling
k-Means clustering
PTAS
Randomized algorithms
Randomized algorithms
D2-sampling
PTAS
k-Means clustering
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ISSN0020-0190
1872-6119
DOI10.1016/j.ipl.2014.07.009

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Summary:We give an improved analysis of the simple D2-sampling based PTAS for the k-means clustering problem given by Jaiswal et al. [3]. The improvement on the running time is from O(nd⋅2O˜(k2/ϵ)) to O(nd⋅2O˜(k/ϵ)). •We give improved analysis of the Jaiswal–Kumar–Sen algorithm [3].•We get a better running time bound using our analysis.•The new analysis does not require the irreducibility property.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2014.07.009