Sweep Methods for Parallel Computational Geometry

Algorithmica (New York)

Volumn 15, Issue 2, 1996, Pages 126-153

  Goodrich, M T ^a   Ghouse, M R ^a   Bright, J ^a  

^a Johns Hopkins University   (United States)

Author keywords

Computational geometry; Constructive solid geometry; Hidden line elimination; Parallel algorithms; Plane sweeping

Indexed keywords

EID: 1542787572     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01941685     Document Type: Article

References (58)

1. K. Abrahamson, N. Dadoun, D. A. Kirpatrick, and T. Przytycka, A Simple Parallel Tree Contraction Algorithm, TR 87-30, Department of Computer Science, University of British Columbia, 1987.
2. A. Aggarwal, B. Chazelle, L. Guibas, C. Ó'Dúnlaing, and C. Yap, Parallel computational geometry, Algorithmica, 3(3) (1988), 293-328.
3. R. J. Anderson and G. L. Miller, Deterministic parallel list ranking, AWOC 88, Lecture Notes in Computer Science, Vol. 319, Springer-Verlag, Berlin, 1988, pp. 81-90.
4. M. J. Atallah, R. Cole, and M. T. Goodrich, Cascading divide-and-conquer: a technique for designing Parallel algorithms, SIAM J. Comput., 18(3) (1989), 499-532.
5. M. J. Atallah and M. T. Goodrich, Efficient parallel solutions to some geometric problems, J. Parallel Distrib. Comput., 3(4), 1986, 492-507.
6. M. J. Atallah, M. T. Goodrich, and S. R. Kosaraju, Parallel algorithms for evaluating sequences of set-manipulation operations, AWOC 88, Lecture Notes in Computer Science, Vol. 319, Springer-Verlag, Berlin, 1988, pp. 1-10.
7. B. G. Baumgart, A polyhedron representation for computer vision, Proc. 1975 AFIPS National Computer Conf., AFIPS Press, 1975, pp. 589-596.
8. J. L. Bentley and D. Wood, An optimal worst case algorithm for reporting intersections of rectangles, IEEE Trans. Comput., 29(7) (1980), 571-576.
9. M. Bern, Hidden surface removal for rectangles, Proc. 4th ACM Symp. on Computational Geometry, 1988, pp. 183-192.
10. A. Borodin and J. E. Hopcroft, Routing, merging, and sorting on parallel models of computation, J. Comput. System Sci., 30(1) (1985), 130-145.
11. R. P. Brent, The parallel evaluation of general arithmetic expressions, J. Assoc. Comput. Mach., 21(2) (1974), 201-206.
12. S. Chandran and D. Mount, Shared memory algorithms and the medial axis transform, Proc. 1987 IEEE Workshop on Computer Architecture for PAMI, 1987.
13. B. Chazelle, Intersecting is easier than sorting, Proc. 16th ACM Symp. on Theory of Computing, 1984, pp. 125-134.
14. B. Chazelle and H. Edelsbrunner, An optimal algorithm for intersecting line segments in the plane, Proc. 29th IEEE Symp. on Foundations of Computer Science, 1988, 590-600.
15. B. Chazelle and L. J. Guibas, Fractional cascading: I. A data structuring technique, Algorithmica, 1(2), 133-162.
16. A. Chow, Parallel algorithms for geometric problems, Ph.D. thesis. Department of Computer Science, University of Illinois, 1980.
17. R. Cole, Parallel merge sort, SlAM J. Comput., 17(4) (1988), 770-785.
18. R. Cole and U. Vishkin, Approximate scheduling, exact scheduling, and applications to parallel algorithms, Proc. 21th IEEE Symp. on Foundations of Computing, 1986, pp. 478-491.
19. J. R. Driscoll, N. Sarnak, D. D. Sleator, and R. E. Tarjan, Making data structures persistent, Proc. 18th ACM Symp. on Theory of Computing, 1986, pp. 109-121.
20. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, New York, 1987.
21. H. Edelsbrunner, H. A. Maurer, F. P. Preparata, A. L. Rosenberg, E. Welzl, and D. Wood, Stabbing line segments, BIT, 22 (1982), 274-281.
22. M. T. Goodrich, A polygonal approach to hidden-line elimination, Proc. 25th Allerton Conf. on Communication, Control, and Computing, 1987, pp. 849-858.
23. M. T. Goodrich, Intersecting line segments in parallel with an output-sensitive number of processors, Proc. 1989 ACM Symp. on Parallel Algorithms and Architectures, 1989, pp. 127-137.
24. M. T. Goodrich, Applying parallel processing techniques to classification problems in constructive solid geometry, Proc. 1st ACM-SIAM Symp. on Discrete Algebra, 1990, pp. 118-128.
25. M. T. Goodrich, M. J. Atallah, and M. Overmars, An input-size/output-size trade-off in the time-complexity of rectilinear hidden surface removal, ICALP '90, to appear.
26. M. T. Goodrich and S. R. Kosaraju, Sorting on a parallel pointer machine with applications to set expression evaluation, Proc. 29th IEEE Symp. on Foundations of Computing, 1989, pp. 190-195.
27. G. H. Güting, An optimal contour algorithm for iso-oriented rectangles, J. Algorithms, 5(1984), 303-326.
28. R. H. Güting and T. Ottmann, New algorithms for special cases of the hidden line elimination problem, Proc. Symp. on Theoretical Aspects of Computer Science, 1985, pp. 161-171.
29. J. E. Hopcroft, and J. D. Ullman, Set merging algorithms, SIAM J. Comput., 2(4) (1973), 294-303.
30. S. R. Kosaraju and A. L. Delcher, Optimal parallel evaluation of tree-structured computations by raking, AWOC 88, Lecture Notes in Computer Science, Vol. 319, Springer-Verlag, Berlin, 1988, pp. 101-110.
31. C. P. Kruskal, Searching, merging, and sorting in parallel computation, IEEE Trans. Comput., 32(10) (1983), 942-946.
32. C. P. Kruskal, L. Rudolph, and M. Snir, The power of parallel prefix, Proc. 1985 Internat. Cotf. on Particle Processing, 1985, pp. 180-185.
33. R. E. Ladner and M. J. Fischer, Parallel prefix computation, J. Assoc. Comput. Mach., (1980), 831-838.
34. D. T. Lee and F. P. Preparata, Computational geometry - a survey, IEEE Trans. Comput., 33(12) (1984), 872-1101.
35. W. Lipski, Jr., and F. P. Preparata, Finding the contour of a union of iso-oriented rectangles, J. Algorithms, 1(1980), 235-246.
36. Y. Matias and U. Vishkin, On parallel hashing and integer sorting, Report UMIACS-TR-90-13, Institute for Advanced Computer Studies, University of Maryland, 1990.
37. K. Mehlhorn, S. Näher, and C. Uhrig, Hidden line elimination for isooriented rectangles, ESPRIT Technical Report 90-25, 1990.
38. G. L. Miller and J. H. Reif, Parallel tree contraction and its application, Proc. 26th IEEE Symp. on Foundations of Computing, 1985, pp. 478-489.
39. G. L. Miller and S. H. Teng, Dynamic parallel complexity of computational circuits, Proc. 19th ACM Symp. on Theory of Computing, 1987, pp. 254-263.
40. D. E. Muller and F. P. Preparata, Finding the intersection of two convex polyhedra, Theoret. Comput. Sci., 7(2) (1978), 217-236.
41. M. S. Paterson and F. F. Yao, Binary partitions with applications to hidden surface removal and solid modeling, Proc. 5th Symp. on Computational Geometry, 1989, pp. 23-32.
42. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
43. F. P. Preparata, J. S. Vitter, and M. Yvinec, Computation of the axial view of a set of isothetic parallelepipeds. Report LIENS-88-1, Dépt. de Math. et d'Info., Lab. d'Informatique de L'Ecole Normal Supérieure, 1988.
44. J. H. Reif and S. Sen, An efficient output-sensitive hidden-surface removal algorithm and its parallelization, Proc. 4th Symp. on Computational Geometry, 1988, pp. 193-200.
45. A. A. G. Requicha, Representations for rigid solids: theory, methods, and systems, ACM Comput. Surveys, 12(4) (1980), 437-464.
46. C. Rüb, Computing intersections and arrangements for red-blue curve segments in parallel, Proc. 4th Canadian Conf. on Computational Geometry, (1992), pp. 115-120.
47. A. Schmitt, On the time and space complexity of certain exact hidden line algorithms, Report 24/81, Fakultät für Informatik, University of Karlsruhe, 1981.
48. Y. Shiloach and U. Vishkin, An O (log n) parallel connectivity algorithm, J. Algorithms, 3 (1982), 57-63.
49. E. Soisalon-Soininen and D. Wood, Optimal algorithms to compute the closure of a set of iso-rectangles, J. Algorithms, 5 (1984), 199-214.
50. I. E. Sutherland, R. F. Sproull, and R. A. Schumacker, A characterization of ten hidden-surface algorithms, Comput. Surveys, 6(1) (1974), 1-25.
51. R. E. Tarjan and U. Vishkin, Finding biconnected components and computing tree functions in logarithmic parallel time, SIAM J. Comput., 14 (1985), 862-874.
52. R. B. Tilove, Set membership classification: a unified approach to geometric intersection problems, IEEE Trans. Comput., 29(10) (1980), 874-883.
53. R. B. Tilove, A null-object detection algorithm for constructive solid geometry, Comm. ACM, 27(7) (1984), 684-694.
54. L. G. Valiant, Parallelism in comparison problems, SMM J. Comput., 4(3) (1975), 348-355.
55. H. Wagener, Optimally parallel algorithms for convex hull determination, Manuscript, 1985.
56. H. Wagener, Optimally parallel hull construction for simple polygons in O (log log n) time, Proc. 33rd IEEE Symp. on Foundations of Computing, 1992, pp. 513-599.
57. P. Widmayer and D. Wood, Time and space-optimal contour computation for a set of rectangles, Inform. Process Lett., 24 (1987), 335-338.
58. D. Wood, The contour problem for rectilinear polygons, Inform. Process Lett., 19 (1984), 229-236.