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Author Har-Peled, Sariel ♦ Raichel, Benjamin
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2015
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Clustering ♦ Linear time ♦ Nets ♦ Optimization
Abstract We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTAS's) to several well known problems in Computational Geometry, such as $\textit{k}-center$ clustering and farthest nearest neighbor. The new approach is robust to variations in the input problem, and yet it is simple, elegant, and practical. In particular, many of these well studied problems which fit easily into our framework, either previously had no linear time approximation algorithm, or required rather involved algorithms and analysis. A short list of the problems we consider include farthest nearest neighbor, $\textit{k}-center$ clustering, smallest disk enclosing $\textit{k}$ points, $\textit{k}th$ largest distance, $\textit{k}th$ smallest $\textit{m}-nearest$ neighbor distance, $\textit{k}th$ heaviest edge in the MST and other spanning forest type problems, problems involving upward closed set systems, and more. Finally, we show how to extend our framework such that the linear running time bound holds with high probability.
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 2015-12-10
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 62
Issue Number 6
Page Count 35
Starting Page 1
Ending Page 35


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Source: ACM Digital Library