A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
Parallel processing for efficient subdivision search
SCG '87 Proceedings of the third annual symposium on Computational geometry
SIAM Journal on Computing
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Towards a theory of nearly constant time parallel algorithms
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems
SIAM Journal on Computing
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An NC parallel 3D convex hull algorithm
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Constructing the Voronoi Diagram of a Set of Line Segments in Parallel (Preliminary Version)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Parallel algorithms for geometric problems
Parallel algorithms for geometric problems
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A Randomized Algorithm for Voronoi Diagram of Line Segments on Coarse-Grained Multiprocessors
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
| Hi-index | 0.00 |
In this paper, we present an optimal parallel randomized algorithm for the Voronoi diagram of a set of n non-intersecting (except possibly at endpoints) line segments in the plane. Our algorithm runs in O(logn) time with very high probability and uses O(n) processors on a CRCW PRAM. This algorithm is optimal in terms of P.T bounds since the sequential time bound for this problem is &OHgr;(nlogn). Our algorithm improves by an O(logn) factor the previously best known deterministic parallel algorithm which runs in O(log2n) time using O(n) processors. We obtain this result by using random sampling at “two stages” of our algorithm and using efficient randomized search techniques. This technique gives a direct optimal algorithm for the Voronoi diagram of points as well (all other optimal parallel algorithms for this problem use reduction from the 3-d convex hull construction).