Time-step optimal broadcasting in mesh networks with minimum total communication distance

We propose a new minimum total communication distance (TCD) algorithm and an optimal TCD algorithm for broadcast in a 2-dimensional mesh (2-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 2-D mesh is partitioned into four 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. These algorithms are extended to a 3-dimensional mesh (3-D mesh), and are 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.