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 α < 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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics