Art gallery theorems and algorithms
Art gallery theorems and algorithms
A parallel algorithm for the visibility problem from a point
Journal of Parallel and Distributed Computing
A bridging model for parallel computation
Communications of the ACM
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
General purpose parallel architectures
Handbook of theoretical computer science (vol. A)
An optimal parallel algorithm for the visibility of a simple polygon from a point
Journal of the ACM (JACM)
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Communication-efficient parallel sorting (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Randomized fully-scalable BSP techniques for multi-searching and convex hull construction
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal Parallel Hypercube Algorithms for Polygon Problems
IEEE Transactions on Computers
A 2-D Parallel Convex Hull Algorithm with Optimal Communication Phases
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
A Convex Hull Algorithm on Coarse-Grained Multiprocessors
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Scalable 2d convex hull and triangulation algorithms for coarse grained multicomputers
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
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We present efficient deterministic parallel algorithmic techniques for solving geometric problems in BSP like coarse-grain network models. Our coarse-grain network techniques seek to achieve scalability and minimization of both the communication time and local computation time. These techniques enable us to solve a number of geometric problems in the plane, such as computing the visibility of non-intersecting line segments, computing the convex hull, visibility, and dominating maxima of a simple polygon, two-variable linear programming, determination of the monotonicity of a simple polygon, computing the kernel of a simple polygon, etc. Our coarse-grain algorithms represent theoretical improvement over previously known results, and take into consideration additional practical features of coarse-grain network computation.