Approximation Algorithms for Projective Clustering (2000)
| Venue: | Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia |
| Citations: | 196 - 14 self |
BibTeX
@INPROCEEDINGS{Agarwal00approximationalgorithms,
author = {Pankaj K. Agarwal and Cecilia M. Procopiuc},
title = {Approximation Algorithms for Projective Clustering},
booktitle = {Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia},
year = {2000}
}
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Abstract
We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyper-strips (resp. hyper-cylinders) so that the maximum width of a hyper-strip (resp., the maximum diameter of a hyper-cylinder) is minimized. Let w be the smallest value so that S can be covered by k hyper-strips (resp. hyper-cylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NP-Hard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...
