A space-optimal data-stream algorithm for coresets in the plane

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2007, Pages 1-10

  Agarwal, Pankaj K ^a   Yu, Hai ^a  

^a Duke University   (United States)

Author keywords

Coresets; Data streams; Extent measures

Indexed keywords

DATA-STREAM ALGORITHMS; EXTENT MEASURES; KERNELS;

ALGORITHMS; DATA REDUCTION; NUMERICAL METHODS; OPTIMAL SYSTEMS; PROBLEM SOLVING;

SET THEORY;

EID: 35348812511     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1247069.1247071     Document Type: Conference Paper

References (23)

1. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan, Approximating extent measures of points, J. ACM, 51 (2004), 606-635.
2. P. K. Agarwal, S. Har-Peled, and H. Yu, Robust shape fitting via peeling and grating coresets, Proc. 17th ACM-SIAM Sympos. Discrete Algorithms, 2006, pp. 182-191.
3. P. K. Agarwal, S. Krishnan, N. Mustafa, and S. Venkatasubramanian, Streaming geometric optimization using graphics hardware, Proc. 11th European Sympos. Algorithms, 2003, pp. 544-555.
4. P. K. Agarwal, N. Mustafa, S. Har-Peled, and Y. Wang, Near-linear time approximation algorithms for curve simplification, Algorithmica, (2005), 203-219.
5. B. Babcock, S. Babu, M. Datar, R. Motwani, and J. Widom, Models and issues in data stream systems, Proc. 21st ACM Sympos. Principles of Database Systems, 2002, pp. 1-16.
6. A. Bagchi, A. Chaudhary, D. Eppstein, and M. Goodrich, Deterministic sampling and range counting in geometric data streams, Proc. 20th Annu. Sympos. Comput. Geom., 2004, pp. 144-151.
7. G. Barequet and S. Har-Peled, Efficiently approximating the minimum-volume bounding box of a point set in three dimensions, J. Algorithms, 38 (2001), 91-109.
8. J. Bentley and J. Saxe, Decomposable searching problems I: Static-to-dynamic transformations, J. Algorithms, 1 (1980), 301-358.
9. T. M. Chan, Faster core-set constructions and data-stream algorithms in fixed dimensions, Comput. Geom. Theory Appl., 35 (2006), 20-35.
10. T. M. Chan and B. Sadjad, Geometric optimization problems over sliding windows, Internat. J. Comput. Geom. Appl., 16 (2006), 145-157.
11. G. Cormode and S. Muthukrishnan, Radial histograms for spatial streams, Tech. Rep., DIMACS, 2003.
12. R. Dudley, Metric entropy of some classes of sets with differentiable boundaries, J. Approx. Theory, 10 (1974), 227-236.
13. J. Feigenbaum, S. Kannan, and J. Zhang, Computing diameter in the streaming and sliding-window models, Algorithmica, 41 (2004), 25-41.
14. G. Frahling, P. Indyk, and C. Sohler, Sampling in dynamic data streams and applications, Proc. 21st Annu. Sympos. Comput. Geom., 2005, pp. 142-149.
15. G. Frahling and C. Sohler, Coresets in dynamic geometric data streams, Proc. 37th Annu. ACM Sympos. Theory Cornput., 2005, pp. 209-217.
16. S. Har-Peled and S. Mazumdar, Coresets for k-means and k-medians and their applications, Proc. 36th Annu. ACM Sympos. Theory Comput., 2004, pp. 291-300.
17. S. Har-Peled and Y. Wang, Shape fitting with outliers, SIAM J. Comput., 33 (2004), 269-285.
18. J. Hershberger and S. Suri, Adaptive sampling for geometric problems over data streams, Proc. 23rd ACM Sympos. Principles of Database Systems, 2004, pp. 252-262.
19. P. Indyk, Streaming algorithms for geometric problems, Proc. 24th Intl. Conf. Foundat. Software Tech. Theoret. Comput. Sci., 2004, pp. 32-34.
20. J. Mitchell and S. Suri, Separation and approximation of polyhedral objects, Proc. 4th ACM-SIAM Sympos. Discrete Algorithms, 1992, pp. 296-306.
21. S. Muthukrishnan, Data Streams: Algorithms and Applications, Now Publishers Inc., 2005.
22. S. Suri, C. Toth, and Y. Zhou, Range counting over multidimensional data streams, Discrete Comput. Geom., (2006), 633-655.
23. H. Yu, P. K. Agarwal, R. Poreddy, and K. R. Varadarajan, Practical methods for shape fitting and kinetic data structures using coresets, Algorithmica, to appear.