Load balancing and locality in hierarchical N-body algorithms on distributed memory architectures

Abstract

An n-body application simulates, at discrete time steps, the evolution of n bodies, each exerting a force on all the other ones. At each time step, n ² forces are computed, where n belongs to the range from 10⁴ to 10⁶. A hierarchical algorithm recursively partitions the space into subcubes and it approximates the force exerted on a body B by all the bodies on a (sub)cube C as the force exerted by one body, whose position is the center of mass of the bodies in C and whose mass is the sum of their masses. The algorithm may be described as the visit of a tree representing the hierarchical relation among subcubes of the whole space. In a distributed memory architecture, the nodes of the tree may replicated or partitioned in the memories of the processing nodes. We show that to reduce both the execution time and the memory utilization, load balancing should assign bodies to the processing nodes taking locality into account, i.e. bodies close to each other should be assigned to processing nodes close to each other. A set of experimental results of the proposed algorithm is presented.