On coresets for k-means and k-median clustering

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2004, Pages 291-300

  Har Peled, Sariel ^a   Mazumdar, Soham ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Clustering; Coreset; k means; k median; Streaming

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; OPTIMIZATION; POLYNOMIALS; PROBABILITY; SET THEORY; THEOREM PROVING;

CLUSTERING; CORESET; K-MEANS; K-MEDIAN; STREAMING;

PROBLEM SOLVING;

EID: 4544303932     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1007352.1007400     Document Type: Conference Paper

References (29)

1. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan. Approximating extent measures of points. J. Assoc. Comput. Mach., 2003. to appear.
2. P. K. Agarwal, C. M. Procopiuc, and K. R. Varadarajan. Approximation algorithms for k-line center. In Proc. 10th Annu. European Sympos. Algorithms, pages 54-63, 2002.
3. A. Amir, A. Efrat, P. Indyk, and H. Samet. Efficient algorithms and regular data structures for dilation, location and proximity problems. In Proc. 40th Annu. IEEE Sympos, Found. Comput. Sci., pages 160-170, 1999.
4. S. Arora. Polynomial time approximation schemes for euclidean tsp and other geometric problems. J. Assoc. Comput. Mach., 45(5)753-782, Sep 1998.
5. S. Arora, P. Raghavan, and S. Rao. Approximation schemes for Euclidean k-median and related problems. In Proc. 30th Annu. ACM Sympos. Theory Comput., pages 106-113, 1998.
6. S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu. An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. Assoc. Comput. Mach., 45(6), 1998.
7. V. Arya, N. Garg, R. Khandekar, K. Munagala, and V. Pandit. Local search heuristic for k-median and facility location problems. In Proc. 33rd Annu. ACM Sympos. Theory Comput., pages 21-29, 2001.
8. M. Bǎdoiu and K. L. Clarkson. Optimal core-sets for balls. In Proc. 14th ACM-SIAM Sympos. Discrete Algorithms, pages 801-802, 2003.
9. M. Bǎdoiu, S. Har-Peled, and P. Indyk. Approximate clustering via core-sets. In Proc. 34th Annu. ACM Sympos. Theory Comput., pages 250-257, 2002.
10. J. L. Bentley and J. B. Saxe. Decomposable searching problems i: Static-to-dynamic transformation. J. Algorithms, 1(4):301-358, 1980.
11. M. Charikar and S. Guha. Improved combinatorial algorithms for the facility location and k-median problems. In Proc. 40th Annu. IEEE Sympos. Found. Comput. Sci., pages 378-388, 1999.
12. M. Charikar, S. Guha, E. Tardos, and D. B. Shrnoys. A constant-factor approximation algorithm for the k-median problem. In Proc. 31st Annu. ACM Sympos. Theory Comput., pages 1-10, 1999.
13. W. F. de la Vega, M. Karpinski, C. Kenyon, and Y. Rabani. Approximation schemes for clustering problems. In Proc. 35th Annu. ACM Sympos. Theory Comput., pages 50-58, 2003.
14. T. Feder and D. H. Greene. Optimal algorithms for approximate clustering. In Proc. 20th Annu. ACM Sympos. Theory Comput., pages 434-444, 1988.
15. M. Golin, R. Raman, C. Schwarz, and M. Smid, Simple randomized algorithms for closest pair problems. Nordic J. Comput., 2:3-27, 1995.
16. T. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoret. Comput. Sci., 38:293-306, 1985.
17. S. Guha, R. M. N. Mishra, and L. O'Callaghan. Clustering data streams. In Proc. 41th Annu. IEEE Sympos. Found. Comput. Sci., pages 359-366, 2000.
18. S. Har-Peled. Clustering motion. In Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci., pages 84-93, 2001.
19. S. Har-Peled. A replacement for Voronoi diagrams of near linear size. In Proc. 42nd Annu. IEEE Sympos. Found. Comput. 3d., pages 94-103, 2001.
20. S. Har-Peled and K. R. Varadarajan. Projective clustering in high dimensions using core-sets. In Proc. 18th Annu. ACM Sympos. Comput. Geom., pages 312-318, 2002.
21. M. Inaba, N. Katoh, and H. Imai. Applications of weighted voronoi diagrams and randomization to variance-based k-clustering. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 332-339, 1994.
22. P. Indyk. Sublinear time algorithms for metric space problems. In Proc. 31st Annu. ACM Sympos. Theory Comput., pages 154-159, 1999.
23. P. Indyk. (1 + ε)-approximate bi-criterion algorithm for k-median on a stream. In Proc. 36th Annu. ACM Sympos. Theory Comput., 2004.
24. K. Jain and V. V. Vazirani. Primal-dual approximation algorithms for metric facility location and k-median problems. In Proc. 40th Annu. IEEE Sympos. Found. Comput. Sci., pages 2-13, 1999.
25. T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu. A local search approximation algorithm for k-means clustering. In Proc. 18th Annu. ACM Sympos. Comput. Geom., pages 10-18, 2002.
26. S. G. Kolliopoulos and S. Rao. A nearly linear-time approximation scheme for the euclidean k-median problem. In Proc. 7th Annu. European Sympos. Algorithms, pages 378-389, 1999.
27. L. O. M. Charikar and R. Panigrahy. Better streaming algorithms for clustering problems. In Proc. 35th Annu. ACM Sympos. Theory Comput., pages 30-39, 2003.
28. J. Matoušek. On approximate geometric k-clustering. Discrete Comput. Geom., 24:61-84, 2000.
29. R. Mettu and C. G. Plaxton. Optimal time bounds for approximate clustering. In In Proceedings of the 18th Conference on Uncertainty in Artifical Intelligence, pages 344-351, 2002.