- Author:
- Michael Truman Goodrich,
- Major Professor:
- Mikhail J. Atallah
In this thesis we present a number of new techniques for solving many of the fundamental problems in computational geometry efficiently in parallel. The resulting algorithms all have linear or "almost" linear speed-ups over the best known sequential algorithms for these problems. Specifically, the problems we address include the following: computing the diameter of a convex polygon, planar convex hull finding, finding a closest pair of points, polygon triangulation, 3-dimensional maxima finding, dominance counting, determining the visibility from a point, trapezoidal decomposition, and planar point location. The techniques presented are quite different from the ones used in the efficient sequential algorithms. All of our results are for the CREW PRAM or EREW PRAM computational models.
Cited By
Chazelle B and Liu D Lower bounds for intersection searching and fractional cascading in higher dimension Proceedings of the thirty-third annual ACM symposium on Theory of computing, (322-329)- Goodrich M Constructing arrangements optimally in parallel (preliminary version) Proceedings of the third annual ACM symposium on Parallel algorithms and architectures, (169-179)
- Atallah M, Callahan P and Goodrich M P-complete geometric problems Proceedings of the second annual ACM symposium on Parallel algorithms and architectures, (317-326)
- Reif J and Sen S Randomized algorithms for binary search and load balancing with geometric applications Proceedings of the second annual ACM symposium on Parallel algorithms and architectures, (327-339)
- Berkman O, Breslauer D, Galil Z, Schieber B and Vishkin U Highly parallelizable problems Proceedings of the twenty-first annual ACM symposium on Theory of computing, (309-319)
- Atallah M and Tsay J On the parallel decomposability of geometric problems Proceedings of the fifth annual symposium on Computational geometry, (104-113)
- Cole R and Goodrich M Optimal parallel algorithms for polygon and point-set problems Proceedings of the fourth annual symposium on Computational geometry, (201-210)
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