Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
An optimal-time algorithm for slope selection
SIAM Journal on Computing
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Intersecting line segments in parallel with an output-sensitive number of processors
SIAM Journal on Computing
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Determining an optimal penetration among weighted regions in two and three dimensions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Optimal Beam Penetrations in Two and Three Dimensions
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
On geometric optimization problems
On geometric optimization problems
Improved Optimal Weighted Links Algorithms
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Computing Optimal Trajectories for Medical Treatment Planning and Optimization
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Parallel Optimal Weighted Links
Transactions on Computational Science III
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In this paper we consider parallel algorithms for computing an optimal link among weighted regions in the 2-dimensional (2-D) space. The weighted regions optimal link problem arises in several areas, such as geographic information systems (GIS), radiation therapy, geological exploration, environmental engineering and military applications. We present a CREW PRAM parallel algorithm and a coarse-grain parallel computer algorithm. Given a weighted subdivision with a total of n vertices, the work of the parallel algorithms we propose is only a O(log n) factor more than that of their (optimal) sequential counterparts.