Broadcasting with linearly bounded transmission faults Original Research Article

We consider broadcasting with a linearly bounded number of transmission failures. For a constant parameter 0 < α < 1 we assume that at most αi faulty transmissions can occur during the first i time units of the communication process, for every natural number i. Every informed node can transmit information to at most one neighbor in a unit of time. Faulty transmissions have no effect. We investigate worst-case optimal non-adaptive broadcasting time under this fault model, for several communication networks. We show, e.g., that for the n-node line network this time is linear in n, if 1/2, and exponential otherwise. For the hypercube and the complete graph, broadcasting in the linearly bounded fault model can be performed in time logarithmic in the number of nodes.