Near-optimal broadcast in all-port wormhole-routed 3D tori with dimension-ordered routing

The one-to-all broadcast is the most primary operation in a multicomputer network. In this paper we study this problem in a wormhole-routed 3D torus which provides the dimension-ordered routing and the all-port communication capability. We propose an efficient scheme to utilize the distance-insensitive characteristic of wormhole routing. The scheme requires at most 4 steps more than the optimal number of steps for any square 3D tools. The best known results, as compared to ours, can only be applied to cubic tori of very restricted network sizes and either rely on an undesirable non-dimension-ordered routing or require more numbers of steps