Parallel solutions to geometric problems in the scan model of computation

Journal of Computer and System Sciences

Volumn 48, Issue 1, 1994, Pages 90-115

  Blelloch, Guy E ^a   Little, James J ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STRUCTURES; GEOMETRY; MATHEMATICAL MODELS; MERGING; PARALLEL PROCESSING SYSTEMS; SCANNING; SORTING; TREES (MATHEMATICS); VECTORS;

BINARY SEARCH TECHNIQUE; CONVEX HULL ALGORITHM; DATA PARALLEL MODEL; DIVIDE AND CONQUER ALGORITHM; GEOMETRIC PROBLEMS; SCAN MODEL; SEGMENT ABSTRACTION;

ALGORITHMS;

EID: 0028371882     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/S0022-0000(05)80023-6     Document Type: Article

References (35)

1. A. Aggarwal, B. Chazelle, L. Guibas, C. Ò’Dúnlaing, and C. Yap, Parallel computational geometry, in “Proceedings, Symposium on Foundations of Computer Science, Oct. 1985,” pp. 468-477.
2. S. G. Akl, Two remarks on a convex hull algorithm, Inform. Process. Lett. 8 (1979), 108-109.
3. M. J. Atallah, R. Cole, and M. T. Goodrich, Cascading divide-and-conquer: A technique for designing parallel algorithms, SIAM J. Comput. 18 (1989), 499-532.
4. M. J. Atallah and M. T. Goodrich, Efficient parallel solutions to some geometric problems, J. Parallel Distrib. Comput. 3 (1986), 492-507.
5. M. J. Atallah and M. T. Goodrich, Efficient plane sweeping in parallel, in “Proceedings, ACM Symposium on Theory of Computing, 1986,” pp. 216-225.
6. J. L. Bentley, Multidimensional binary search trees used for associative searching, Commun. ACM 18 (1975), 509-517.
7. J. L. Bentley and M. I. Shamos, Divide-and-conquer in multidimensional space, in “Proceedings, ACM Symposium on Theory of Computing, 1976,” pp. 220-230.
8. G. E. Blelloch, Scans as primitive parallel operations, IEEE Trans. Comput. C38 (1989), 1526-1538.
9. G. E. Blelloch, “Vector Models for Data-Parallel Computing,” MIT Press, Cambridge, MA, 1990.
10. G. E. Blelloch and S. Chatterjee, VCODE: A data-parallel intermediate language, in “Proceedings, Frontiers of Massively Parallel Computation, Oct. 1990.
11. A. Borodin, On relating time and space to size and depth, SIAM J. Comput. 6 (1977), 733-744.
12. R. P. Brent, The parallel evaluation of general arithmetic expressions, J. Assoc. Comput. Mach. 21 (1974), 201-206.
13. S. Chatterjee, G. E. Blelloch, and M. Zagha, Scan primitives for vector computers, in “Proceedings, Supercomputing’90, Nov. 1990.
14. R. Cole, Parallel merge sort, SIAM J. Comput. 17 (1988), 770-785.
15. R. Cole and M. T. Goodrich, Optimal parallel algorithms for point-set and polygon problems, in “Proceedings, Fourth Annual Symposium on Computational Geometry, 1988.
16. R. Cole and U. Vishkin, Deterministic coin tossing and accelerating cascades: Micro and macro techniques for designing parallel algorithms, in “Proceedings, ACM Symposium on Theory of Computing, 1986,” pp. 206-219.
17. S. A. Cook, A taxonomy of problems with fast parallel algorithms, Inform, and Control 64 (1985), 2-22.
18. S. Fortune and J. Wyllie, Parallelism in random access machines, in “Proceedings, ACM Symposium on Theory of Computing, 1978,” pp. 114-118.
19. H. Freeman, Computer processing of line-drawing images, Comput. Surveys 6 (1974), 57-97.
20. J. H. Friedman, J. L. Bentley, and R. A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Trans. Math. Software 3 (1977), 209-226.
21. L. M. Goldschlager, A universal interconnection pattern for parallel computers, J. Assoc. Comput. Mach. 29 (1982), 1073-1086.
22. J. G. Hocking and G. S. Young, “Topology,” Addison-Wesley, Reading, MA, 1961.
23. R. A. Jarvis, On the identification of the convex hull on a finite set of points in the plane, Inform. Process. Lett. 2 (1973), 18-21.
24. R. E. Ladner and M. J. Fischer, Parallel prefix computation, J. Assoc. Comput. Mach. 27 (1980), 831-838.
25. R. Miller and Q. F. Stout, Efficient parallel convex hull algorithms, IEEE Trans. Comput. 37 (1988), 1605-1618.
26. W. M. Newman and R. F. Sproull, “Principles of Interactive Computer Graphics,” McGraw-Hill, New York, 1979.
27. S. M. Omohundro, Efficient algorithms with neural network behavior, Complex Systems 1 (1987).
28. M. H. Overmars and J. Van Leeuwen, Maintenance of configurations in the plane, J. Comput. System Sci. 23 (1981), 166-204.
29. V. R. Pratt and L. J. Stockmeyer, A characterization of the power of vector machines, J. Comput. System Sci. 12 (1976), 198-221.
30. F. P. Preparata and M. I. Shamos, “Computational Geometry—An Introduction,” Springer- Verlag, New York, 1985.
31. J. H. Reif and S. Sen, Optimal randomized parallel algorithms for computational geometry, in “Proceedings, International Conference on Parallel Processing, August 1987,” pp. 270-277.
32. J. B. Salem, “*Render: A Data Parallel Approach to Polygon Rendering,” Tech. Rep. VZ88-2, Thinking Machines Corporation, Jan. 1988.
33. J. T. Schwartz, Ultracomputers, ACM Trans. Programming Lang. Systems 2 (1980), 484-521.
34. Y. Shiloach and U. Vishkin, Finding the maximum, merging and sorting in a parallel computation model, J. Algorithms 2 (1981), 88-102.
35. L. G. Valiant, Universal circuits (preliminary report), in “Proceedings, ACM Symposium on Theory of Computing, 1976,” pp. 196-202.