Fault-tolerant minimum broadcast networks

Broadcasting is the task of transmitting a message originated at one processor of a communication network to all other processors in the network. A minimal k-fault-tolerant broadcast network is a communication network on n vertices in which any processor can broadcast in spite of up to k line failures in optimal time Tn(k). In this paper, we study Bk(n), the minimum number of communication lines of any minimal k-fault-tolerant broadcast network on n processors. We give the value of Bk(n) for several values of n and k and, in case k < [log n], give almost-minimum k-fault-tolerant broadcast networks.