Faster core-set constructions and data stream algorithms in fixed dimensions

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2004, Pages 152-159

  Chan, Timothy M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Approximation algorithms; Data streams; Geometric optimization problems

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; DATA REDUCTION; DATA STRUCTURES; OPTIMIZATION;

APPROXIMATION ALGORITHMS; DATA STREAMS; GEOMETRIC OPTIMIZATION PROBLEMS;

COMPUTATIONAL GEOMETRY;

EID: 4544222520     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/997817.997843     Document Type: Conference Paper

References (31)

1. P. K. Agarwal, B. Aronov, and M. Sharir. Line transversals of balls and smallest enclosing cylinders in three dimensions. Discrete Comput. Geom., 21:373-388, 1999.
2. P. K. Agarwal, L. J. Guibas, S. Har-Peled, A. Rabinovitch, and M. Sharir. Computing the penetration depth of two convex polytopes in 3D. Nordic J. Comput., 7:227-240, 2000.
3. P. K. Agarwal, S. Krishnan, N. H. Mustafa, and S. Venkatasubramanian. Streaming geometric optimization using graphics hardward. In Proc. 11th European Sympos. Algorithms, Lect. Notes Comput. Sci., vol. 2832, Springer-Verlag, pages 544-555, 2003.
4. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan. Approximating extent measures of points, http://-valis.cs.uiuc.edu/~sariel/research/papers/01/-fitting/, 2003. Preliminary versions appeared in Proc. 12th ACM-SIAM Sympos. Discrete Algorithms, pages 148-157, 2001; Proc. 42nd IEEE Sympos. Found. Comput. Sci., pages 66-73, 2001.
5. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan. Approximating extent measures of points, http://-valis.cs.uiuc.edu/~sariel/research/papers/01/-fitting/, 2003. Preliminary versions appeared in Proc. 12th ACM-SIAM Sympos. Discrete Algorithms, pages 148-157, 2001; Proc. 42nd IEEE Sympos. Found. Comput. Sci., pages 66-73, 2001.
6. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan. Approximating extent measures of points, http://-valis.cs.uiuc.edu/~sariel/research/papers/01/-fitting/, 2003. Preliminary versions appeared in Proc. 12th ACM-SIAM Sympos. Discrete Algorithms, pages 148-157, 2001; Proc. 42nd IEEE Sympos. Found. Comput. Sci., pages 66-73, 2001.
7. P. K. Agarwal, J. Matoušek, and S. Suri. Farthest neighbors, maximum spanning trees and related problems in higher dimensions. Comput. Geom. Theory Appl., 1:189-201, 1992.
8. S. Arya, T. Malamatos, and D. M. Mount. Space-efficient approximate Voronoi diagrams. In Proc. 34th ACM Sympos. Theory Comput., pages 721-730, 2002.
9. M. Bǎdoiu and K. L. Clarkson. Optimal core-sets for balls, http://cm.bell-labs.com/who/clarkson/-pubs.html, 2003. Preliminary version in Proc. 14th ACM-SIAM Sympos. Discrete Algorithms, pages 801-802, 2003.
10. M. Bǎdoiu and K. L. Clarkson. Optimal core-sets for balls, http://cm.bell-labs.com/who/clarkson/-pubs.html, 2003. Preliminary version in Proc. 14th ACM-SIAM Sympos. Discrete Algorithms, pages 801-802, 2003.
11. M. Bǎdoiu, S. Har-Peled, and P. Indyk. Approximate clustering via core-sets. In Proc. 34th ACM Sympos. Theory Comput., pages 250-257, 2002.
12. G. Barequet and S. Har-Peled. Efficiently approximating the minimum-volume bounding box of a point set in three dimensions. J. Algorithms, 38:91-109, 2001.
13. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Heidelberg, 1997.
14. H. Breu, J. Gil, D. Kirkpatrick, and M. Werman. Linear time Euclidean distance transform algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17:529-533, 1995.
15. E. M. Bronshteyn and L. D. Ivanov. The approximation of convex sets by polyhedra. Siberian Math. J., 16:852-853, 1976.
16. T. M. Chan. Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus. Int. J. Comput. Geom. Appl. 12:67-85, 2002.
17. R. M. Dudley. Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory, 10:227-236, 1974.
18. C. A. Duncan, M. T. Goodrich, and E. A. Ramos. Efficient approximation and optimization algorithms for computational metrology. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 121-130, 1997.
19. J. Feigenbaum, S. Kannan, and J. Zhang. Computing diameter in the streaming and sliding-window models. Technical report YALEU/DCS/TR-1245, Yale University. 2002. Algorithmica, to appear.
20. S. Har-Peled. A practical approach for computing the diameter of a point-set. In Proc. 17th ACM Sympos. Comput. Geom., pages 177-186, 2001.
21. S. Har-Peled. A replacement for Voronoi diagrams of near linear size. In Proc. 42nd IEEE Sympos. Found. Comput. Sci., pages 94-103, 2001.
22. S. Har-Peled and K. Varadarajan. High-dimensional shape fitting in linear time. In Proc. 19th ACM Sympos. Comput. Geom., pages 39-47, 2003.
23. S. Har-Peled and Y. Wang. Shape fitting with outliers. SIAM J. Comput., 33:269-285, 2004.
24. M. Henzinger, P. Raghavan, and S. Rajagopalan. Computing on data streams. Technical Note 1998-011, Digital Systems Research Center. Palo Alto, CA, 1998.
25. J. Hershberger and S. Suri. Convex hulls and related problems in data streams. ACM SIGMOD/PODS Workshop on Management and Processing of Data Streams (MPDS), http://www.research.att.com/-conf/mpds2003/schedule/, 2003.
26. R. Janardan. On maintaining the width and diameter of a planar point-set online. Int. J. Comput. Geom. Appl., 3:331-344, 1993.
27. G. Malandain and J.-D. Boissonnat, Computing the diameter of a point set. Int. J. Comput. Geom. Appl., 12:489-510, 2002.
28. S. Muthukrishnan. Data streams: algorithms arid applications. http://www.cs.rutgers.edu/~muthu/, 2003.
29. G. Rote, C. Schwarz, and J. Snoeyink. Maintaining the approximate width of a set of points in the plane. In Proc. 5th Canad. Conf. Comput. Geom., pages 258-263, 1993.
30. J. O'Rourke. Finding minimal enclosing boxes. Internat. J. Comput. Info. Sci., 14:183-199, 1986.
31. O. Schwarzkopf. Parallel computation of distance transforms. Algorithmica, 6:685-697, 1991.