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
Optimizing the sum of linear fractional functions
Recent advances in global optimization
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Minimal link visibility paths inside a simple polygon
Computational Geometry: Theory and Applications
Geometric bicriteria optimal path problems
Geometric bicriteria optimal path problems
Finding an approximate minimum-link visibility path inside a simple polygon
Information Processing Letters
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Parallel Optimal Weighted Links
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Approximate shortest paths in anisotropic regions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing a shortest k-link path in a polygon
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On finding approximate optimal paths in weighted regions
Journal of Algorithms
k-link shortest paths in weighted subdivisions
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
In this paper we consider parallel algorithms for computing an optimal link among weighted regions in the plane. The problem arises in several areas, including radiation therapy, geological exploration and environmental engineering. We present a CREW PRAM parallel algorithm and a coarse-grain parallel computer algorithm for this problem. For a weighted subdivision with n vertices, the work of the parallel algorithms we propose is only an O (logn ) factor more than that of their optimal sequential counterparts. We further adapt an algorithm for minimizing sum of linear fractionals, that has inherent parallelism, to solve in parallel the global optimization problems associated with our solution for the weighted region optimal link problem.