Bi-criteria linear-time approximations for generalized k-mean/median/center

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2007, Pages 19-26

  Feldman, Dan ^a   Fiat, Amos ^a   Sharir, Micha ^a   Segev, Danny ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Approximation; Bi criteria approximation; Geometric optimization; K center; K mean; K median

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; FUNCTION EVALUATION; LINEAR SYSTEMS; OPTIMIZATION; RANDOM PROCESSES;

BI-CRITERIA APPROXIMATION; GEOMETRIC OPTIMIZATION; K-CENTER; K-MEAN; K-MEDIAN;

SET THEORY;

EID: 35348816131     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1247069.1247073     Document Type: Conference Paper

References (24)

1. P.K. Agarwal, S. Har-Peled and K. R. Varadarajan, Geometrie approximation via coresets, in Combinatorial and Computational Geometry, Cambridge University Press, New York, Vol. 52, pp. 1-30, 2005.
2. P. K. Agarwal and N. H. Mustafa, k-Means projective clustering, Proc. 23rd Annu. ACM Symposium on Principles of Database Systems, 2004, pp.155-165.
3. P. K. Agarwal and C. M. Procopiuc, Approximation algorithms for projective clustering, Proc. 11th Annu. ACM-SIAM Symposium on Discrete Algorithms, 2000, pp. 538-547.
4. P. K. Agarwal, C. M. Procopiuc and K. R. Vaeadarajan, Approximation algorithms for k-line center, Proc. 10th Annu. European Symposium on Algorithms, Vol. 2461, Lecture Notes Comput. Sci., 2002, pp. 54-63.
5. C. C. Aggarwal, C. M. Procopiuc, J. L. Wolf, and P. S. Yu, Fast algorithms for projected clustering, Proc. ACM-SIGMOD Intl. Conf. Managment of Data, 1999, pp. 61-72.
6. C.C. Aggarwal and P. S. Yu, Finding generalized projected clusters in high dimensional spaces, Proc. A CM-SIGMOD Intl. Conf. on Management of Data, 2000, pp. 544-555.
7. R. Agrawal, J. Gehrke, D. Gunopulos and P. Raghavan, Automatic subspace clustering of high-dimensional data for data mining applications, Proc. ACM-SIGMOD Intl. Conf. on Management of Data, 1998, pp. 94-105.
8. A. Deshpande, L. Rademacher, S. Vempala and G. Wang, Matrix approximation and projective clustering via volume sampling, Proc. 17th Annu. ACM-SIAM Symposium on Discrete Algorithms, 2006, pp. 1117-1126.
9. A. Deshpande and S. Vempala, Adaptive Sampling and Fast Low-Rank Matrix Approximation, Proc. 10th International Workshop on Randomization and Computation, RANDOM 2006, pp. 292-303.
10. T. K. Dey, Improved bounds for planar k-sets and related problems, Discrete Comput. Geom. 19 (1998), 373-382.
11. D. Feldman, A. Fiat and M. Sharir, Coresets for weighted facilities and their applications, Proc. 47th Annu. IEEE Symposium on Foundations of Computer Science, 2006, pp. 315-324.
12. D. Feldman, M. Monemizadeh, and C. Sohler, Coresets with negative weightes and their applications for high dimensional clustering, manuscript, 2007.
13. S. Har-Peled, Clustering motion, Proc. 42nd Annu. IEEE Symposium on Foundations of Computer Science, 2001, pp. 84-93.
14. S. Har-Peled, Low rank matrix approximation in linear time, Manuscript, 2006.
15. S. Har-Peled and S. Mazumdar, On coresets for k-means and k-median clustering, Proc. 36th Annu. ACM Symposium on Theory of Computing, 2004, pp. 291-300.
16. S. Har-Peled and K. Varadarajan, Projective clustering in high dimensions using coresets, Proc. 18th Annu. ACM Symposium on Computational Geometry, 2002, pp. 312-318.
17. P, Indyk, Sublinear time algorithms for metric space problems, Proc. 31st Annu. ACM Symposium on Theory of Computing, 1999, pp. 428-434.
18. J. W. Jaromczyk and M. Kowaluk, The two-line center problem from a polar view: A new algorithm and data structure, Lecture Notes in Computer Science, Vol. 955, Springer Verlag, 1995, pp. 13-18.
19. N. Megiddo and A. Tamir, Finding least distance lines, SIAM J. Algebraic Discrete Methods 4 (1983), 207-211.
20. R. Panigrahy, Minimum enclosing polytope in high dimensions, Computing Research Repository, cs.CG/0407020, 2004.
21. K. Pearson, On lines and planes of closest fit to systems of points in space. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 1901, pp. 559-572.
22. C. M. Procopiuc, M. Jones, P. K. Agarwal and T. M. Murali, A Monte Carlo algorithm for fast projective clustering, Proc. ACM SIGMOD Intl. Conf. on Management of Data, 2002, pp. 418-427.
23. T. Sarlós, Improved approximation algorithms for large matrices via random projections, Proc. 47th Annu. IEEE Symposium on Foundations of Computer Science, 2006, pp. 143-152.
24. N. D. Shyamalkumar and K. R. Varadarajan, Efficient subspace approximation algorithm, Proc. 18th Annu. ACM-SIAM Symposium on Discrete Algorithms, 2007.