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 independent 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(long2n) time algorithms for solving the next element search problem, the trapezoidal composition problem, and the triangulation problem