Computational geometry: an introduction
Computational geometry: an introduction
An O(log n) time parallel algorithm for triangulating a set of points in the plane
Information Processing Letters
An optimal parallel algorithm for triangulating a set of points in the plane
International Journal of Parallel Programming
Efficient parallel solutions to some geometric problems
Journal of Parallel and Distributed Computing
Finding the convex hull of a sorted point set in parallel
Information Processing Letters
Triangulating a monotone polygon in parallel
Proceedings on International Workshop on Computational Geometry on Computational Geometry and its Applications
Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
SIAM Journal on Computing
Adaptive bitonic sorting: an optimal parallel algorithm for shared-memory machines
SIAM Journal on Computing
Triangulating a polygon in parallel
Journal of Algorithms
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Highly parallelizable problems
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Optimal parallel algorithms for polygon and point-set problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Optimal merging and sorting on the EREW PRAM
Information Processing Letters
An optimal parallel algorithm for the visibility of a simple polygon from a point
Journal of the ACM (JACM)
Planar separators and parallel polygon triangulation (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Testing a simple polygon for monotonicity optimally in parallel
Information Processing Letters
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
Parallel Dictionaries in 2-3 Trees
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Optimal Parallel Algorithms for Finding Proximate Points, with Applications
IEEE Transactions on Parallel and Distributed Systems
On Computing the Upper Envelope of Segments in Parallel
IEEE Transactions on Parallel and Distributed Systems
Optimal Parallel Hypercube Algorithms for Polygon Problems
IEEE Transactions on Computers
Parallelizability of Some P-Complete Problems
IPDPS '00 Proceedings of the 15 IPDPS 2000 Workshops on Parallel and Distributed Processing
Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce
Proceedings of the 19th international conference on World wide web
Recursion and parallel algorithms in geometric modeling problems
Cybernetics and Systems Analysis
The system of common algorithmic space to create visual models of phenomena and processes
Proceedings of the International Conference on Applications of Computer and Information Sciences to Nature Research
A parallel algorithm for finding all successive minimal maximum subsequences
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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We present a technique that can be used to obtain efficient parallel geometric algorithms in the EREW PRAM computational model. This technique enables us to solve optimally a number of geometric problems in O(log n) time using O(n/log n) EREW PRAM processors, where n is the input size of a problem. These problems include: computing the convex hull of a set of points in the plane that are given sorted, computing the convex hull of a simple polygon, computing the common intersection of half-planes whose slopes are given sorted, finding the kernel of a simple polygon, triangulating a set of points in the plane that are given sorted, triangulating monotone polygons and star-shaped polygons, and computing the all dominating neighbors of a sequence of values. PRAM algorithms for these problems were previously known to be optimal (i.e., in O(log n) time and using O(n/log n) processors) only on the CREW PRAM, which is a stronger model than the EREW PRAM