Parallel Processing Symposium, International (1997)
Apr. 1, 1997 to Apr. 5, 1997
We present a parallel algorithm for solving the next element search problem on a set of line segments, using a BSP like model referred to as the Coarse Grained Multicomputer (CGM). The algorithm requires O(1) communication rounds (h-relations with h=O(n/p)), O((n/p) log n) local computation, and O((n/p) log n) storage per processor. Our result implies solutions to the point location, trapezoidal decomposition and polygon triangulation problems. A simplified version for axis parallel segments requires only O(n/p) storage per processor, and we discuss an implementation of this version.As in a previous paper by Develliers and Fabri, our algorithm is based on a distributed implementation of segment trees which are of size O(n log n). This paper improves on which presented a CGM algorithm for the special case of trapzoidal decomposition only and requires O((n/p) * log p * log n) local computation.
A. Rau-Chaplin, A. Chan and F. Dehne, "Coarse Grained Parallel Next Element Search," Parallel Processing Symposium, International(IPPS), Geneva, SWITZERLAND, 1997, pp. 320.