Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima

Journal of Parallel and Distributed Computing

Volumn 63, Issue 4, 2003, Pages 488-500

  Gupta, Neelima ^a   Sen, Sandeep ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038009787     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0743-7315(03)00035-2     Document Type: Article

References (25)

1. N.M. Amato, M.T. Goodrich, E.A. Ramos, Parallel algorithms for higher-dimensional convex hulls, Proceedings of the 35th Annual FOCS, Santa Fe, NM, 1994, pp. 683-694.
2. N.M. Amato, F.P. Preparata, The parallel 3d convex hull problem revisited, Internat. J. Comput. Geom. Appl. 2 (2) (1992) 163-173.
3. N.M. Amato, E.M. Ramos, On computing vornoi diagrams by divide-prune-and-conquer, ACM Symposium on Computational Geometry, Vol. 12, Philadelphia, PA, 1996 pp. 166-175.
4. M.J. Atallah, R. Cole, M.T. Goodrich, Cascading divide-and-conquer: a technique for designing parallel algorithms, SIAM J. Comput. 18 (1989) 499-532.
5. H. Bast, T. Hagerup, Fast parallel space allocation, estimation and integer sorting, Technical Report, MPI-I-93-123, 1993.
6. R. Brent, Parallel evaluation of general arithmetic expressions, J. ACM 21 (1974) 201-206
7. T.M. Chan, Output-sensitive results on convex hulls, extreme points and related problems, ACM Symposium on Computational Geometry, 1995.
8. B. Chazelle, J. Matoušek, Derandomizing an output-sensitive convex-hull algorithm in three dimensions, Tech Report, Princeton University, 1992.
9. A. Chow, Parallel algorithms for geometric problems, Ph.D. Thesis, University of Illinois, Urbana-Champaign, 1980.
10. K.L. Clarkson, P.W. Shot, Applications of random sampling in computational geometry ii, Discrete Comput. Geom. 4 (1989) 387-421.
11. N. Dadoun, D.G. Kirkpatrick, Parallel construction of subdivision hierarchies, J. Comput. System Sci. 39 (1989) 153-165.
12. M. Ghouse, M.T. Goodrich, In-place techniques for parallel convex-hull algorithm, Proceedings of the Third ACM Symposium on Parallel Algorithms Architecture, Hilton Head, SC, 1991, pp. 192 203.
13. M.T. Goodrich, Geometric partitioning made easier, even in parallel, Proceedings of the Nineth ACM Symposium on Computational Geometry, San Diego, CA, 1993, pp. 73-82.
14. N. Gupta, S. Sen, Faster output-sensitive parallel convex hulls for d ∞lt; 3: optimal sublogarithmic algorithms for small outputs, ACM Symposium on Computational Geometry, 1996, pp. 176-185.
15. N. Gupta, S. Sen, Optimal, output-sensitive algorithms for constructing planar hulls in parallel, Comput. Geom.: Theory Appl. 8 (1997) 151-166.
16. T. Hagerup, R. Raman, Waste makes haste: tight bounds for loose parallel sorting, FOCS 33 (1992) 628-637.
17. D. Haussler, E. Welzl, E-nets and simplex range queries, Discrete Comput. Geom. 2 (2) (1987) 127-152.
18. M. Ketan, Computational Geometry: An Introduction through Randomized Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1994.
19. D.G. Kirkpatrick, R. Seidel, The ultimate planar convex hull algorithm, SIAM J. Comput. 15 (1) (1986) 287 299.
20. J. Matoušek, Linear optimization queries, ACM Symposium on Computational Geometry, Vol. 8, Berlin, Germany, 1992, pp. 16-25.
21. F.P. Preparata, S.J. Hong, Convex hulls of finite sets of points in two and three dimensions, Comm. ACM 20 (1977) 87-93.
22. S. Rajasekaran, S. Sen, in: J.H. Reif (Ed.), Random Sampling Techniques and Parallel Algorithm Design, Morgan, Kaufman, Los Altos, CA, 1993.
23. J.H. Reif, S. Sen, Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems, Siam J. Comput. 21 (3) (1992) 466-485.
24. R. Seidel, Constructing higher-dimensional convex hulls at logarithmic cost per face, Proceedings of the ACM Annual Symposium on Theory of Computing, Vol. 18, Berkeley, CA, 1986, pp. 404-413.
25. S. Sen, Lower bounds for algebraic decision trees, parallel complexity of convex hulls and related problems, Theoret. Comput. Sci. 188 (1997) 59-78.