Near-optimal broadcast in all-port wormhole-routed hypercubes using error-correcting codes

A new broadcasting method is presented for hypercubes with wormhole routing mechanism. The communication model assumed allows an n-dimensional hypercube to have at most n concurrent I/O communication along its ports. It assumes a distance insensitivity of (n + 1) with no intermediate reception capability for the nodes. The approach is based on determination of the set of nodes called stations in the hypercube. Once stations are identified, node disjoint paths are formed from the source to all stations. The broadcasting is accomplished first by sending the message to all stations, which will inform the rest of the nodes. To establish node-disjoint paths between the source node and all stations, we introduce a new routing strategy. We prove that multicasting can be done in one routing step as long as the number of destination nodes are at most n in an n-dimensional hypercube. The number of broadcasting steps using our routing is equal to or smaller than that obtained in an earlier work; this number is optimal for all hypercube dimensions n ≤ 12, except for n = 10