In-place techniques for parallel convex hull algorithms

Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1991

Volumn , Issue , 1991, Pages 192-203

  Ghouse, Mujtaba R ^a   Goodrich, Michael T ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; PARALLEL ALGORITHMS;

3-DIMENSIONAL; CONVEX HULL; CONVEX HULL ALGORITHM; HIGH PROBABILITY; OPTIMAL NUMBER; RE ORDERINGS;

PARALLEL ARCHITECTURES;

EID: 85027122396     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. Aggarwal, A., Chazelle, B., Guibas, L., O'Dunlaing.C, and Yap, C, "Parallel Computational Geometry, " Proc. 26th IEEE FOCS (1985), pp.468-477.
2. N. Alon and N. Megiddo, "Parallel Linear Programming in Fixed Dimension Almost Surely in Constant Time", Proc. 31st IEEE FOCS Symposium (1990), pp. 574-582.
3. Andrew, A.M., "Another efficient algorithm for convex hulls in two dimensions, " Info. Proc. Lett. 9, (1979) pp.216-219.
4. Avis, D., "On the complexity of finding the convex hull of a set of points, " Report SOCS 79.2, (1979), School of Computer Science, McGill University
5. Atallah, M. J., and Goodrich, M. T., "Efficient Parallel Solutions to Some Geometric Problems, " Journal of Parallel and Distributed Computing, 3 (1986), pp. 492-507.
6. Atallah, M. J., and Goodrich, M. T., "Parallel Algorithms for Some Functions of Two Convex Polygons", Algorithmica 3 (1988), pp. 535-548.
7. Bentley, J. L., Faust, G. M., and Preparata, F. P., "Approximation algorithms for convex hulls, " Comm. ACM 25, (1982) pp.64-68.
8. Berkman, O., Breslauer, D., Galil, Z., Schieber, B., and Vishkin, U., "Highly Parallelizable Problems, " Proc. 21st ACM STOC (1989), pp.309-319.
9. O. Berkman and U. Vishkin, "Recursive Star-Tree Parallel Data-Structure", UMIACS-TR-90-40 CS-TR-2437, University of Maryland Institute of Advanced Computer Studies (1990).
10. Chand, D.R., and Kapur, S.S., "An algorithm for convex polytopes, " J ACM 17(1), (1970), pp.78-86.
11. ChernofF, H., "A measure of asymptotic efficiency for tests of a hypothesis based on the sum of the observations, " Annals of Math. Stat., 23 (1952), pp. 493-509.
12. Chow, A., "Parallel Algorithms for Geometric Problems, " PhD dissertation, Computer Science Department, University of Illinois at Urbana-Champagne, 1980.
13. Cole, R., and Vishkin, U., "Approximate and exact parallel scheduling with applications to list, tree and graph problems, " Proc. 27th IEEE FOCS, (1986) pp.478-491. pp.128-142.
14. Cole, R., Zajicek, O., "An Optimal Parallel Algorithm for Building a Data Structure for Planar Point Location", J. Parallel and Distributed Computing 8 (1990) pp. 280-285.
15. Dadoun, N., and Kirkpatrick, D.G., "Parallel Construction of Subdivision Hierarchies, " Tech. Report 87-13 (1987), Department of Computer Science, University of British Columbia.
16. H. Edelsbrunner and W. Shi, "An O(n log h) Time Algorithm for the Three-dimensional Convex Hull Problem", SIAM J. on Computing 20 (1991), pp. 259-269.
17. Eppstein, D., and Galil, Z., "Parallel Algorithmic Techniques for Combinatorial Computation", Ann. Rev. Comput. Sci., 3, pp. 233-283.
18. Graham, R.L., "An efficient algorithm for determining the convex hull of a planar set, " Info. Proc. Lett. 1, (1972) pp.132-133.
19. Jarvis, R.A., "On the identification of the convex hull of a finite set of points in the plane, " Info. Proc. Lett. 2, (1973) pp. 18-21.
20. Karloff, H. J., and Raghavan, P., "Randomized Algorithms and Pseudorandom Numbers", Proc. 20th ACM STOC (1988), pp. 310-321.
21. Kirkpatrick, D., G., and Seidel, R., " The ultimate planar convex hull algorithm?", SIAM J. Comput. 15 (1), (1986), pp. 287-299.
22. Ladner, R. E., Fischer, M. J., "Parallel prefix computation, " J ACM 27 (1980), pp. 831-838.
23. Mathews, "Number Theory", Chelsea Publications, New York, (1961).
24. Matias, Y., and Vishkin, U., "Converting High Probability into Nearly-Constant Time - with Applications to Parallel Hashing", to appear in Proc. 23rd ACM STOC (1991).
25. Miller, R., and Stout, Q., F., "Parallel Algorithms for convex hulls, " Proc. Comp. Vision and Pat. Recogn. (1988).
26. Overmars, M.H., van Leeuwen, J., "Maintenance of configurations in the plane, " J. Comput. and Syst. Sci. 23 (1981), pp.166-204.
27. Preparata, F. P., and Shamos, M. I., "Computational Geometry An Introduction", published by Springer-Verlag (1985).
28. Ragde, P., "The Parallel Simplicity of Compaction and Chaining, " Proc. 11th International Colloquium on Automata, Languages and Programming (ICALP), Springer-Verlag Lecture Notes in Computer Science: 443, 1990, 744-751.
29. Raghavan, P., "Lecture Notes on Randomized Algorithms", unpublished manuscript.
30. Reif, J. H., and Sen, S., "Polling: A New Randomized Sampling Technique For Computational Geometry", Proc. 21st ACM STOC (1989) pp. 394-404.
31. Seidel, R., "A convex hull algorithm optimal for points in even dimensions, " M. S. Thesis, Tech. Rep. 81-14, (1981) Dept. of Comput. Sci., Univ. of British Columbia, Vancouver, Canada.
32. R. Seidel, "Output-Size Sensitive Algorithms for Constructive Problems in Computational Geometry", (PhD Thesis) TR 86-784, Department of Computer Science, Cornell University, (1986), pp 15-16.
33. Stout, Q. F., "Constant-Time Geometry on PRAMs", Proc. of the 17th International Conference on Parallel Processing 1988, pp 104-107.
34. Yao, A.C., "A lower bound to finding convex hulls, " J. ACM 28 (1981) pp.780-787.