Computational Geometry on the Broadcast Communication Model

In this paper, we solve three geometric problems, including the ranking, convex hull and closest pair problems, under the broadcast communication model. To solve these problems, we propose a general scheme, the p-division approach, which is based upon the divide-and-conquer strategy. In the 2-dimensional space, the time complexities of our algorithms for solving these problems are all (The equation is abbreviated), where n is the number of input points and p is the number of processors used. Furthermore, our algorithms are all conflict-free and optimal. In the k-dimensional space, k≥3, our ranking algorithm requires (The equation is abbreviated) time.