Parallel algorithms for some dominance problems based on a CREW PRAM

Abstract

Two parallel geometric algorithms based on the idea of point domination are presented. The first algorithm solves the d-dimensional isothetic rectangles intersection counting problem of input size N/2 ^d, where d > 1 and N is a multiple of 2^d, in O(log^d−1 N) time and O(N) space. The second algorithm solves the direct dominance reporting problem for a set of N points in the plane in O(log N+J) time and O(N log N) space, where J denotes the maximum of the number of direct dominances reported by any single point in the set. Both algorithms make use of the CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) consisting of O(N) processors as the computational model.