Computational geometry: an introduction
Computational geometry: an introduction
Intersection of convex objects in two and three dimensions
Journal of the ACM (JACM)
Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Optimal parallel algorithms for polygon and point-set problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
Deterministic sorting in nearly logarithmic time on the hypercube and related computers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
An optimal parallel algorithm for the visibility of a simple polygon from a point
Journal of the ACM (JACM)
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Testing a simple polygon for monotonicity optimally in parallel
Information Processing Letters
Efficient Geometric Algorithms on the EREW PRAM
IEEE Transactions on Parallel and Distributed Systems
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
Parallel permutation and sorting algorithms and a new generalized connection network
Journal of the ACM (JACM)
Parallel Geometric Algorithms in Coarse-Grain Network Models
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
| Hi-index | 14.98 |
We present parallel techniques on hypercubes for solving optimally a class of polygon problems. We thus obtain optimal O(log n)-time, n-processor hypercube algorithms for the problems of computing the portions of an n-vertex simple polygonal chain C that are visible from a given source point, computing the convex hull of C, testing an n-vertex simple polygon P for monotonicity, and other related problems as well. Previously it was not known how to achieve these complexity bounds on hypercubes, one of the main difficulties being that there is no known optimal sorting hypercube algorithm that achieves these bounds. In fact these are the first optimal geometric hypercube algorithms that do not assume that the input is given already sorted by x or y coordinates. The hypercube model we use is the standard one, with O(1) local memory per processor, and with one-port communication.