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