Reliable Broadcasting in Hypercubes with Random Link and Node Failures

Abstract

We consider the problem of broadcasting in ann–node hypercube whose links and nodes fail independently with given probabilities p < 1 and q < 1, respectively. Information held in a fault-free node, called thesource, has to reach all other fault-free nodes. Messages may be directly transmitted to adjacent nodes only, and every node may communicate with at most one neighbour in a unit of time. A message can be transmitted only if both communicating neighbours and the link joining them are fault-free. For parameterspandqsatisfying (1 –p)(1 –q) ≽ 0.99 (e.g.p=q= 0.5%), we give an algorithm working in timeO(logn) and broadcasting source information to all fault-free nodes with probability exceeding 1 –cn-efor some positive constantε, cdepending onpandqbut not depending onn.