On Approximate Geometric k -Clustering |
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Authors: | J Matoušek |
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Institution: | (1) Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic matousek@kam.mff.cuni.cz, CZ |
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Abstract: | For a partition of an n -point set into k subsets (clusters) S
1
,S
2
,. . .,S
k
, we consider the cost function , where c(S
i
) denotes the center of gravity of S
i
. For k=2 and for any fixed d and ε >0 , we present a deterministic algorithm that finds a 2-clustering with cost no worse than (1+ε) -times the minimum cost in time O(n log n); the constant of proportionality depends polynomially on ε . For an arbitrary fixed k , we get an O(n log
k
n) algorithm for a fixed ε , again with a polynomial dependence on ε .
Received October 19, 1999, and in revised form January 19, 2000. |
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Keywords: | |
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