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41st Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for geometric kclustering
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
R. Ostrovsky, Y. Rabani, "Polynomial time approximation schemes for geometric kclustering," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 349, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892123, author = {R. Ostrovsky and Y. Rabani}, title = {Polynomial time approximation schemes for geometric kclustering}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {349}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892123}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Polynomial time approximation schemes for geometric kclustering SN  02725428 SP EP A1  R. Ostrovsky, A1  Y. Rabani, PY  2000 KW  computational complexity; computational geometry; pattern clustering; polynomial time approximation schemes; geometric kclustering; data point clustering; distance function; data set partitioning; NPhard problem; high dimensional geometry; binary cube; Hamming distance; kmedian problem VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We deal with the problem of clustering data points. Given n points in a larger set (for example, R/sup d/) endowed with a distance function (for example, L/sup 2/ distance), we would like to partition the data set into k disjoint clusters, each with a "cluster center", so as to minimize the sum over all data points of the distance between the point and the center of the cluster containing the point. The problem is provably NPhard in some high dimensional geometric settings, even for k=2. We give polynomial time approximation schemes for this problem in several settings, including the binary cube (0, 1)/sup d/ with Hamming distance, and R/sup d/ either with L/sup 1/ distance, or with L/sup 2/ distance, or with the square of L/sup 2/ distance. In all these settings, the best previous results were constant factor approximation guarantees. We note that our problem is similar in flavor to the kmedian problem (and the related facility location problem), which has been considered in graphtheoretic and fixed dimensional geometric settings, where it becomes hard when k is part of the input. In contrast, we study the problem when k is fixed, but the dimension is part of the input. Our algorithms are based on a dimension reduction construction for the Hamming cube, which may be of independent interest.
Index Terms:
computational complexity; computational geometry; pattern clustering; polynomial time approximation schemes; geometric kclustering; data point clustering; distance function; data set partitioning; NPhard problem; high dimensional geometry; binary cube; Hamming distance; kmedian problem
Citation:
R. Ostrovsky, Y. Rabani, "Polynomial time approximation schemes for geometric kclustering," focs, pp.349, 41st Annual Symposium on Foundations of Computer Science, 2000
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