Scalable 2D Convex Hull and Triangulation Algorithms for Coarse Grained Multicomputers

Abstract

In this paper we describe scalable parallel algorithms for building the convex hull and a triangulation ofncoplanar points. These algorithms are designed for thecoarse grained multicomputermodel:pprocessors withO(n/p)⪢O(1) local memory each, connected to some arbitrary interconnection network. They scale over a large range of values ofnandp, assuming only thatn⩾p1+ε(ε>0) and require timeO((Tsequential/p)+Ts(n,p)), whereTs(n,p) refers to the time of a global sort ofndata on approcessor machine. Furthermore, they involve only a constant number of global communication rounds. Since computing either 2D convex hull or triangulation requires timeTsequential=Θ(nlogn) these algorithms either run in optimal time,Θ((nlogn)/p), or in sort time,Ts(n,p), for the interconnection network in question. These results become optimal whenTsequential/pdominatesTs(n,p) or for interconnection networks like the mesh for which optimal sorting algorithms exist.