Optimal Parallel Hypercube Algorithms for Polygon Problems

IEEE Transactions on Computers

Volumn 44, Issue 7, 1995, Pages 914-922

  Atallah, Mikhail J ^a   Chen, Danny Z ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Algorithms; computational geometry; convex hulls; hypercubes; kernel; monotonicity; simple polygons; visibility

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; MATHEMATICAL MODELS; OPTIMAL SYSTEMS; PROBLEM SOLVING; SET THEORY; SORTING;

COMPLEXITY BOUNDS; CONVEX HULLS; OPTIMAL PARALLEL HYPERCUBE ALGORITHMS; SIMPLE POLYGONAL CHAIN;

PARALLEL ALGORITHMS;

EID: 0029343918     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.392849     Document Type: Article

References (23)

1. M.J. Atallah, D.Z. Chen, and H. Wagener, “An optimal parallel algorithm for the visibility of a simple polygon from a point,” J. ACM, vol. 38, pp. 516-533, 1991.
2. M.J. Atallah, R. Cole, and M.T. Goodrich, “Cascading divide-and-conquer: A technique for designing parallel algorithms,” SIAM J. Computing, vol. 18, no. 3, pp. 499-532, 1989.
3. K. Batcher, “Sorting networks and their applications,” Proc. AFIPS Spring Joint Computing Conf., vol. 32, pp. 307-314, 1968.
4. B. Chazelle and D.P. Dobkin, “Intersection of convex objects in two and three dimensions,” J. ACM, vol. 34, no. 1, pp. 1-27, 1987.
5. D.Z. Chen, “Efficient geometric algorithms on the EREW-PRAM,” Proc. 28th Ann. Allerton Conf. on Comm., Control, and Computing, pp. 818-827, 1990; also IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 1, pp. 41-47, 1995.
6. D.Z. Chen and S. Guha, ‘Testing a simple polygon for monotonicity optimally in parallel,” Information Processing Letters, vol. 47, no. 6, pp. 325-331, 1993.
7. R. Cole and M.T. Goodrich, “Optimal parallel algorithms for polygon and point-set problems,” Proc. Fourth Ann. ACM Symp. Computational Geometry, pp. 211-220, 1988; also Algorithmica, vol. 7, no. 1, pp. 3-23,1992
8. R. Cypher and C.G. Plaxton, “Deterministic sorting in nearly logarithmic time on the hypercube and related computers,” Proc. 22nd Ann. ACM Symp. Theory of Computing, pp. 193-203, 1990.
9. J.A. Dean and J.R. Sack, “Efficient hidden-line elimination by capturing winding information,” Proc. 23rd Ann. Allerton Conference on Communication, Control, and Computing, pp. 496-505, 1985.
10. F. Dehne, A. Ferreira, and A. Rau-ChapHn, “Parallel fractional cascading on a hypercube multiprocessor,” Proc. 27th Ann. Allerton Conf. Comm., Control, and Computing, Monticello, III., pp. 1,084-1,093, 1989.
11. F. Dehne and A. Rau-Chaplin, “Implementing data structures on a hypercube multiprocessor, with applications in parallel computational geometry,” J. Parallel Distributed Computing, vol. 8, pp. 367-375, 1990.
12. H. ElGindy and D. Avis, “A linear algorithm for computing the visibility polygon from a point,” J. Algorithms, vol. 2, pp. 186-197, 1981.
13. R.L. Graham and F.F. Yao, “Finding the convex hull of a simple polygon,” J. Algorithms, vol. 4, no. 4, pp. 324-331, 1983.
14. B. Joe and R.B. Simpson, “Corrections to Lee's visibility polygon algorithm,” BIT, vol. 27, pp. 458-473, 1987.
15. D.T. Lee, “Visibility of a simple polygon,” Computer Vision, Graphics, and Image Processing, vol. 22, pp. 207-221, 1983.
16. D.T. Lee, “On finding the convex hull of a simple polygon,” Int'l J. Computing and Information Science, vol. 12, no. 2, pp. 87-98,1983.
17. D.T. Lee and F.P. Preparata, “An optimal algorithm for finding the kernel of a polygon,” J. ACM, vol. 26, pp. 415-421, 1979.
18. F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays-Trees-Hypercubes, Morgan Kaufmann, San Mateo, Calif., 1992.
19. P.D. MacKenzie and Q. Stout, “Asymptotically efficient hypercube algorithms for computational geometry,” Proc. Third Symp. the Frontiers of Massively Parallel Computation, pp. 8-11, 1990.
20. R. Miller and Q.F. Stout, “Efficient parallel convex hull algorithms,” lEEETrans. Computers, vol. 37, no. 12, pp. 1,605-1,618, 1988.
21. D. Nassimi and S. Sahni, “Parallel permutation and sorting algorithms and a new generalized connection network,” J. ACM, vol. 29, pp. 642-667, 1982.
22. F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, New York, 1985.
23. F.P. Preparata and K.J. Supowit, ‘Testing a simple polygon for monotonicity,” Information Processing Letters, vol. 12, pp. 161-164, 1981.