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Sublinear-time approximation algorithms for clustering via random sampling
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Czumaj, Artur and Sohler, Christian (2007) Sublinear-time approximation algorithms for clustering via random sampling. In: 12th International Conference on Random Structures and Algorithms, Poznan, POLAND, AUG 01-05, 2005. Published in: RANDOM STRUCTURES & ALGORITHMS, 30 (1-2 Sp. Iss. SI). pp. 226-256.
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Official URL: http://dx.doi.org/10.1002/rsa.20157
Abstract
We present a novel analysis of a random sampling approach for four clustering problems in metric spaces: k-median, k-means, min-sum k-clustering, and balanced k-median. For all these problems, we consider the following simple sampling scheme: select a small sample set of input points uniformly at random and then run some approximation algorithm on this sample set to compute an approximation of the best possible clustering of this set. Our main technical contribution is a significantly strengthened analysis of the approximation guarantee by this scheme for the clustering problems. The main motivation behind our analyses was to design sublinear-time algorithms for clustering problems. Our second contribution is the development of new approximation algorithms for the aforementioned clustering problems. Using our random sampling approach, we obtain for these problems the first time approximation algorithms that have running time independent of the input size, and depending on k and the diameter of the metric space only. (c) 2006 Wiley Periodicals, Inc.
| Item Type: | Conference Item (UNSPECIFIED) |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Computer Science |
| Journal or Publication Title: | RANDOM STRUCTURES & ALGORITHMS |
| Publisher: | JOHN WILEY & SONS INC |
| ISSN: | 1042-9832 |
| Date: | January 2007 |
| Volume: | 30 |
| Number: | 1-2 Sp. Iss. SI |
| Number of Pages: | 31 |
| Page Range: | pp. 226-256 |
| Identification Number: | 10.1002/rsa.20157 |
| Publication Status: | Published |
| Title of Event: | 12th International Conference on Random Structures and Algorithms |
| Location of Event: | Poznan, POLAND |
| Date(s) of Event: | AUG 01-05, 2005 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/32489 |
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