Minimizing total communication distance of a time-step optimal broadcast in mesh networks

In this paper, we propose a new minimum total communication distance (TCD) algorithm and an optimal TCD algorithm for broadcast in a 2-dimension 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 can be generalized to a d-dimensional mesh or torus. TCD can potentially be used as a measurement for other types of collective communication operations.