An Optimal Fault-Tolerant Nonredundant Broadcasting Scheme in Injured Hypercubes

Abstract

We propose a nonredundant broadcasting scheme for injured hypercube multicomputers with direct-connection capability, that is, where each hypercube node has a separate router. The proposed scheme is first presented to cover faulty links only. Under the assumption that no more than n − 1 faulty links exist in an injured n-cube, the proposed scheme is optimal in the sense that it generates a spanning binomial tree from a given node whenever there exists such a tree originated from that node. The scheme is also extended to cover both node and link faults. Although the extended scheme is no longer optimal, we show that by using the extended scheme the maximum number of routing steps required from the source node s to any other node a is H( s, a) + 2, where H stands for the Hamming distance. The proposed scheme uses global network information. Evaluation studies show that the proposed scheme achieves optimal broadcasting a high percentage of times.