Hypercube algorithms for parallel processing of pointer-based quadtrees

This paper studies the parallel construction and manipulation of pointer-based quadtrees on fine grained hypercube multiprocessors. Previous papers considered the parallel processing of linear quadtrees. Here we show that parallel pointer-based quadtrees are a viable alternative. We first solve the problem of efficiently constructing a pointer-based (or linear) quadtree from an image represented either by a binary matrix or a boundary code. Then we present efficient parallel manipulation algorithms for pointer-based quadtrees, such as finding the neighbors of all leaves in a quadtree or computing the union/intersection of two quadtrees. These algorithms improve on existing time complexities and can be implemented in fine grained hypercube systems (e.g., the Connection Machine CM2). In the expected case, the space complexity is the same as for previous methods. In the worst case (of a degenerated quadtree), the space complexity increases by a factor which, for the hypercube, is smaller than the time complexity improvement. As a byproduct of our hypercube algorithms, we also obtain some PRAM algorithms for quadtrees that improve on known results