Technical Reports (CIS)
Document Type
Technical Report
Date of this Version
December 1993
Abstract
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(log n) 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 Ω(n log n). Our algorithm improves by an O(log n) factor the previously best known deterministic parallel algorithm which runs in O(log2 n) time using O(n) processors [13]. 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).
Recommended Citation
Sanguthevar Rajasekaran and Suneeta Ramaswami, "Optimal Parallel Randomized Algorithms for the Voronoi Diagram of Line Segments in the Plane and Related Problems", . December 1993.
Date Posted: 16 July 2007
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-93-99.