Counting colors in boxes

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 785-794

  Kaplan, Haim ^a   Rubin, Natan ^a   Sharir, Micha ^a,b   Verbin, Elad ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COLOR; DATA STRUCTURES; DIGITAL STORAGE;

FAST MATRIX MULTIPLICATION; GENERALIZED MATRIX; HIGHER DIMENSIONS; MATRIX MULTIPLICATION; POLYLOGARITHMIC; RANDOM INPUT; SPACE-TIME TRADEOFFS; TIME SPACE TRADEOFFS;

MATRIX ALGEBRA;

EID: 84969135590     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. J. L. Bentley, H. T. Kung, M. Schkolnick, and C. D. Thompson, On the average number of maxima in a set of vectors and applications, J. ACM 25 (1978), 536-543.
2. M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd Edition, Springer Verlag, Heidelberg, 2000.
3. J.-D. Boissonnat, M. Sharir, B. Tagansky and M. Yvinec, Voronoi diagrams in higher dimensions under certain polyhedral distance functions, Discrete Comput. Geom. 19 (1998), 485-519.
4. P. Bozanis, N. Kitsios, C. Makris, and A. Tsakalidis, New upper bounds for generalized intersection searching problems, Proc. 22nd International Colloquium on Automata, Languages and Programming, volume 944 of Lecture Notes in Computer Science, pages 464-475, Berlin,1995, Springer-Verlag.
5. P. Bozanis, N. Kitsios, C. Makris, and A. Tsakalidis, New results on intersection query problems, The Computer Journal 40 (1997), 22-29.
6. P. Bozanis, N. Kitsios, C. Makris, and A. Tsakalidis, Red-blue intersection reporting for objects of nonconstant size, The Computer Journal 39 (1996), 541-546.
7. T. Chan, Dynamic subgraph connectivity with geometric applications, Proc. 34th ACM Sympos. Theory Comput. (2002), 7-13.
8. L. P. Chew, D. Dor, A. Efrat, and K. Kedem, Geometric pattern matching in d-dimensional space, Discrete and Computational Geometry 21 (1999), 257-274.
9. K. L. Clarkson and P. W. Shor, Applications of random sampling in computational geometry II, Discrete Comput. Geom. 4 (1989), 387-421.
10. D. Coppersmith. Rectangular matrix multiplication revisited, J. Complexity 13(1997):42-49.
11. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions, J. Symb. Comput. 9(1990),251-280.
12. D. Gupta, R. Janardan and M. Smid, Computational geometry: Generalized intersection searching, Chapter 64 in Handbook of Data Structures and Applications, D. Mehta and S. Sahni (editors), Chapman & Hall/CRC, Boca Raton, FL, 64-1-64-17, 2005.
13. D. Gupta, R. Janardan and M. Smid, A technique for adding range restrictions to generalized searching problems, Information Procesing Letters 69 (1999), 7-13.
14. D. Gupta, R. Janardan and M. Smid, Algorithms for some intersection searching problems involving circular objects, International Journal of Mathematical Algorithms 1 (1999), 35-52.
15. D. Gupta, R. Janardan and M. Smid, Algorithms for generalized halfspace range searching and other intersection searching problems, Computational Geometry: Theory and Applications, 5 (1996), 321-340.
16. D. Gupta, R. Janardan and M. Smid, Further results on generalized intersection problems: Counting, Reporting, and Dynamization, Journal of Algorithms 19 (1995), 282-317.
17. S. Har-Peled, On the expected complexity of random convex hulls. Technical Report 330/98, School Math. Sci., Tel-Aviv Univ., Tel-Aviv, Israel, 1998.
18. X. Huang and V.Y. Pan. Fast rectangular matrix multiplication and applications. J. Complexity 14 (1998), 257-299.
19. R. Janardan and M. Lopez. Generalized intersection searching problems, International Journal of Computational Geometry and Applications, 3 (1993), 39-69.
20. H. Kaplan, N. Rubin, M. Sharir and E. Verbin, Counting colors in boxes, http://www.cs.tau.ac.il/~rubinnat/clb.pdf.
21. H. Kaplan, M. Sharir and E. Verbin, Colored intersection searching via sparse rectangular matrix multiplication, Proc. 22th ACM Symp. on Computational Geometry (2006), 52-60.
22. R. Yuster and U. Zwick, Fast sparse matrix multiplication, ACM Trans. Algorithms 1 (2005), 2-13.