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 hypercu be to have at most n concurrent I/O communications along its ports. It furt her assumes a distance insensitivity of (n + 1) with no intermediate recept ion capability for the nodes along the communication path. The approach is based on determination of the set of nodes (called stations) in the hypercu be such that for any node in the network there is a station at distance of at most 1. Once stations are identified, parallel disjoint paths are formed from the source to all stations. The broadcasting is accomplished first by sending the message to all stations which will in turn inform the rest of the nodes of the message. To establish node-disjoint paths between the sour ce node and all stations, we introduce a new routing strategy. We prove tha t multicasting can be done in one routing step as long as the number of des tination nodes are at most n in an n-dimensional hypercube. The number of b roadcasting steps using our routing is equal to or smaller than that obtain ed in an earlier work; this number is optimal for all hypercube dimensions n less than or equal to 12, except for n = 10.