Coarse grained parallel next element search

Abstract

The authors 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. The 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 they discuss an implementation of this version. As in a previous paper by Develliers and Fabri (1993), their algorithm is based on a distributed implementation of segment trees which are of size O(n log n). The paper improves on the work of Develliers and Fabri which presented a CGM algorithm for the special case of trapezoidal decomposition only and requires O((n/p)*log p*log n) local computation.