Time-Step Optimal Broadcasting in 3-D Meshes with Minimum Total Communication Distance

In this paper we propose a new minimum total communication distance (TCD) algorithm and anoptimal TCD algorithm for broadcast in a 3-dimensional mesh (3-D mesh). The former generatesa minimum TCD from a given source node, and the latter guarantees a minimum TCD among allthe possible source nodes. These algorithms are based on a divide-and-conquer approach where a3-D mesh is partitioned into eight submeshes of equal size. The source node sends the broadcastmessage to a special node called an eye in each submesh. The above procedure is then recursivelyapplied in each submesh. These algorithms can be generalized to a d-dimensional mesh or torus.In addition, the proposed approach can potentially be used to solve optimization problems in othercollective communication operations.