Determining weak visibility of a polygon from an edge in parallel

International Journal of Computational Geometry and Applications

Volumn 8, Issue 3, 1998, Pages 277-304

  Chen, Danny Z ^a,b  

^a University of Notre Dame   (United States)

^b Purdue University   (United States)

Author keywords

Computational geometry; CREW PRAM; Parallel algorithms; Simple polygons; Weak visibility

Indexed keywords

EID: 0032329311     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021819599800014X     Document Type: Article

References (43)

1. A. Aggarwal, S. Moran, P. W. Shor, and S. Suri, "Computing the minimum visible vertex distance between two polygons," Proc. 1st Workshop on Algorithms and Data Structures, 1989, pp. 115-134.
2. N. M. Amato, "Determining the separation of simple polygons," International J. of Computational Geometry and Applications, 4 (4) (1994), pp. 457-474.
3. N. M. Amato, "Finding a closest visible vertex pair between two polygons," Algorithmica, 14 (2) (1995), pp. 183-201.
4. M. J. Atallah and M. T. Goodrich, "Parallel algorithms for some functions of two convex polygons," Algorithmica, 3 (1988), pp. 535-548.
5. M. J. Atallah, D. Z. Chen, and H. Wagener, "An optimal parallel algorithm for the visibility of a simple polygon from a point," J. of the ACM, 38 (3) (1991), pp. 516-533.
6. D. Avis and G. T. Toussaint, "An optimal algorithm for determining the visibility polygon from an edge," IEEE Trans. Computers, C-30 (12) (1981), pp. 910-914.
7. B. K. Bhattacharya, D. G. Kirkpatrick, and G. T. Toussaint, "Determining sector visibility of a polygon," Proc. 5th Annual ACM Symp. Computational Geometry, 1989, pp. 247-254.
8. B. K. Bhattacharya and A. Mukhopadhyay, "Computing in linear tune an internal line segment from which a simple polygon is weakly internally visible," Proc. 6th Annual International Symp. Algorithms and Computation, 1995, Cairns, Australia.
9. B. K. Bhattacharya, A. Mukhopadhyay, and G. T. Toussaint, "A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visible," Proc. Workshop on Algorithms and Data Structures, 1991, pp. 412-424.
10. B. Chazelle, "Triangulating a simple polygon in linear time," Discrete & Computational Geometry, 6 (1991), pp. 485-524.
11. B. Chazelle and L. J. Guibas, "Visibility and intersection problems in plane geometry," Discrete & Computational Geometry, 4 (1989), pp. 551-581.
12. D. Z. Chen, "Parallel techniques for paths, visibility, and related problems," Ph.D. thesis, Technical Report No. 92-051, Department of Computer Sciences, Purdue University, July 1992.
13. D. Z. Chen, "Determining weak external visibility of polygons in parallel," Proc. 6th Canadian Conf. on Computational Geometry, 1994, pp. 375-380.
14. D. Z. Chen, "Efficient geometric algorithms on the EREW-PRAM," IEEE Trans. Parallel and Distributed Systems, 6 (1) (1995), pp. 41-47.
15. D. Z. Chen, "An optimal parallel algorithm for detecting weak visibility of a simple polygon," International J. of Computational Geometry and Applications, 5 (1 & 2) (1995), pp. 93-124.
16. D. Z. Chen, "Optimally computing the shortest weakly visible subedge for a simple polygon," J. of Algorithms, 20 (3) (1996), pp. 459-478.
17. Y. T. Ching, M. T. Ko, and H. Y. Tu, "On the cruising guard problems," Technical Report, 1989, Institute of Information Science, Academia Sinica, Taipei, Taiwan.
18. G. Das, P. Heffernan, and G. Narasimhan, "Finding all weakly-visible chords of a polygon in linear time," Proc. 4th Scandinavian Workshop on Algorithm Theory, 1994, pp. 119-130.
19. G. Das and G. Narasimhan, "Optimal linear-time algorithm for the shortest illuminating line segment in a polygon," Proc. 10th Annual ACM Symp. Computational Geometry, 1994, pp. 259-266.
20. H. ElGindy, "Hierarchical decomposition of polygon with applications," Ph.D. thesis, McGill University, 1985.
21. H. ElGindy and M. T. Goodrich, "Parallel algorithms for shortest path problems in polygons," The Visual Computer, 3 (6) (1988), pp. 371-378.
22. S. K. Ghosh, A. Maheshwari, S. P. Pal, S. Saluja, and C. E. V. Madhavan, "Characterizing and recognizing weak visibility polygons," Computational Geometry: Theory and Applications, 3 (1993), pp. 213-233.
23. M. T. Goodrich, "Finding the convex hull of a sorted point set in parallel," Information Processing Letters, 26 (1987/88), pp. 173-179.
24. M. T. Goodrich, "Triangulating a polygon in parallel," J. of Algorithms, 10 (1989), pp. 327-351.
25. M. T. Goodrich, "Planar separators and parallel polygon triangulation," J. of Computer and Systems Sciences, 51 (3) (1995), pp. 374-389.
26. M. T. Goodrich, S. B. Shauck, and S. Guha, "Parallel methods for visibility and shortest path problems in simple polygons," Algorithmica, 8 (1992), pp. 461-486.
27. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan, "Linear time algorithms for visibility and shortest path problems inside triangulated simple polygons," Algorithmica, 2 (1987), pp. 209-233.
28. P. J. Heffernan and J. S. B. Mitchell, "Structured visibility profiles with applications to problems in simple polygons," Proc. 6th Annual ACM Symp. Computational Geometry, 1990, pp. 53-62.
29. J. Hershberger, "Optimal parallel algorithms for triangulated simple polygons," Proc. 8th Annual ACM Symp. Computational Geometry, 1992, pp. 33-42.
30. J. Hershberger and S. Suri, "Matrix searching with the shortest path metric," Proc. 25th Annual ACM Symp. Theory of Computing, 1993, pp. 485-494.
31. F. R. Hsu, R. C. Chang, and R. G. T. Lee, "Parallel algorithms for computing the closest visible vertex pair between two polygons," International J. of Computational Geometry and Applications, 1 (2) (1992), pp. 135-162.
32. Y. Ke, "Detecting the weak visibility of a simple polygon and related problems," manuscript, Dept. of Computer Science, The Johns Hopkins University, 1988.
33. C. P. Kruskal, L. Rudolph, and M. Snir, "The power of parallel prefix," IEEE Trans. Computers, C-34 (1985), pp. 965-968.
34. R. E. Ladner and M. J. Fischer, "Parallel prefix computation," J. of the ACM, 27 (4) (1980), pp. 831-838.
35. D. T. Lee and A. K. Lin, "Computing the visibility polygon from an edge," Computer Vision, Graphics, and Image Processing, 34 (1986), pp. 1-19.
36. D. T. Lee and F. P. Preparata, "An optimal algorithm for finding the kernel of a polygon," J. of the ACM, 26 (1979), pp. 415-121.
37. M. H. Overmars and J. van Leeuwen, "Maintenance of configurations in the plane," J. of Computer and Systems Sciences, 23 (1981), pp. 166-204.
38. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, New York, 1985.
39. J.-R. Sack and S. Suri, "An optimal algorithm for detecting weak visibility of a polygon," IEEE Trans. Computers, C-39 (10) (1990), pp. 1213-1219.
40. G. T. Toussaint, "A linear-time algorithm for solving the strong hidden-line problem in a simple polygon," Pattern Recognition letters, 4 (1986), pp. 449-451.
41. G. T. Toussaint and D. Avis, "On a convex hull algorithm for polygons and its applications to triangulation problems," Pattern Recognition, 15 (1) (1982), pp. 23-29.
42. G. A. Wang and E. P. F. Chan, "Finding the minimum visible vertex distance between two nonintersecting simple polygons," Proc. 2nd Annual ACM Symp. Computational Geometry, 1986, pp. 34-42.
43. C. K. Yap, "Parallel triangulation of a polygon in two calls to the trapezoidal map," Algorithmica, 3 (1988), pp. 279-288.