Fast-fault-tolerant parallel communication and on-line maintenance using information dispersal

Space-efficient Information Dispersal Algorithm (IDA) [ll] is applied to parallel communication in the hypercube. Let N denote the size of the network. Our communication scheme runs in 2.1og N + 1 time’ using constant size buffers. Its probability of successful routing is at least 1 _ N-2.419’logN+1.5 proving Rabin’s conjecture. The same scheme also tolerates O(N) random link failures with high probability. The scheme runs within the said time bound without long delay. On-line and efficient wire testing and replacement on the hypercube can be realized if our fault-tolerant routing scheme is used. Let cr denote the total number of links in the hypercube. It is shown that z a/352 wires can be disabled simultaneously without disrupting the ongoing computation or degrading the routing performance much.

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