Hypercube Algorithms for Direct N-Body Solvers for Different Granularities

Abstract

Algorithms for the N-body problem are compared and contrasted, particularly those where N is in the range for which direct methods outperform approximation methods. With fewer bodies than processors, the so-called “replicated orrery” on a three-dimensional grid has been used successfully on the Connection Machine CM-2 architecture. With more bodies, the “rotated and translated Gray codes” is an ideal direct algorithm for machines such as the CM-2 in that it takes optimal advantage of the communications bandwidth of the machine.A classical Latin square can be used to abstractly denote any direct N-body calculation. Computational windows superimposed on this square illustrate the granularity of the computation. This point of view naturally illustrates a sequence of algorithms ranging along a granularity scale in the following order: “massively parallel,” “replicated orrery,” “orrery,” “rotated/translated Gray codes,” and “serial.”