Optimal Parallel Algorithms for Quadtree Problems

Abstract

In this paper we describe optimal processor-time parallel algorithms for set operations such as union, intersection, comparison on quadtrees. The algorithms presented in this paper run in O(log N) time using N/log N processors on a shared memory model of computation that allows concurrent reads or writes. Consequently they allow us to achieve optimal speedups using any number of processors up to N/log N. The approach can also be used to derive optimal processor-time parallel algorithms for weaker models of parallel computation.