The performance of data-parallel algorithms for spatial operations using data-parallel variants of the bucket PMR quadtree, R-tree, and R+-tree spatial data structures is compared. The studied operations are datastructure build, polygonization, and spatial join in an application domainconsisting of planar line segment data i.e., Bureau of the Census TIGER Line les. The algorithms are implemented using the scan model of parallel computation on the hypercube architecture of the Connection Machine. The results of experiments reveal that the bucket PMR quadtree outperforms both the R-tree and R+-tree. This is primarily because the bucket PMR quadtree yields a regular disjoint decomposition of space while the R-tree and R+-tree do not. The regular disjoint decomposition increases the potential for interprocessor communication and parallelism in the bucket PMR quadtree, thereby enabling the execution times to decrease relative to those needed by the R-tree and R+-tree.
Erik G. Hoel, Hanan Samet