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Issue No.03 - March (2000 vol.11)

pp: 247-260

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.841741

ABSTRACT

<p><b>Abstract</b>—A new broadcasting method is presented for hypercubes with wormhole routing mechanism. The communication model assumed allows an <tmath>$n$</tmath>-dimensional hypercube to have at most <tmath>$n$</tmath> concurrent I/O communications along its ports. It further assumes a distance insensitivity of <tmath>$(n+1)$</tmath> with no intermediate reception capability for the nodes along the communication path. The approach is based on determination of the set of nodes (called stations) in the hypercube 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 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 <tmath>$n$</tmath> in an <tmath>$n$</tmath>-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 <tmath>$n \leq 12$</tmath>, except for <tmath>$n=10$</tmath>.</p>

INDEX TERMS

Broadcasting, hamming codes, hypercubes, multicasting, perfect codes, wormhole routing.

CITATION

Hyosun Ko, Shahram Latifi, Pradip K. Srimani, "Near-Optimal Broadcast in All-Port Wormhole-Routed Hypercubes Using Error-Correcting Codes",

*IEEE Transactions on Parallel & Distributed Systems*, vol.11, no. 3, pp. 247-260, March 2000, doi:10.1109/71.841741