Implementing Data Structures on a Hypercube Multiprocessor, and Applications in Parallel Computational Geometry

In this paper, we study the problem of implementing standard data structures on a hypercube multiprocessor. We present a technique for efficiently executing multiple independant search processes on a class of graphs called ordered h-level graphs. We show how this technique can be utilized to implement a segment tree on a hypercube, thereby obtaining O(log2n) time algorithms for solving the next element search problem, the trapezoidal decomposition problem, the triangulation problem, and the (multiple) planar point location problem.