Optimal broadcasting in faulty hypercubes

The problem of broadcasting information in an n-node hypercube in which links fail independently with fixed probability 0 < p < 1 is considered. Information originally held by one node has to be disseminated throughout the network. Messages can be transmitted along links, and in a unit of time every node can transmit to at most one neighbor. Transmissions via faulty links do not succeed. A broadcasting algorithm that disseminates information throughout the whole network in time a log n with probability exceeding 1 - bn^-c with positive constants a,b,c depending on p, provided that p ≤ 9%, is developed. The algorithm works in expected time O(log n) using an expected number of transmissions O(n), and the probability of disseminating information throughout the network converges to 1 as n grows.