Circuit-switched broadcasting in torus and mesh networks

We consider the problem of broadcasting on torus and mesh networks using circuit-switched, half-duplex, and link-bound communication. In this paper, we obtain an optimal broadcasting algorithm that uses pd time steps for a d-dimensional torus with (2d+1)^p nodes in each side of the torus. Using this algorithm, we show that a broadcasting on a d-dimensional mesh with the same size can be done in pd+p+d-1 time steps