Adaptive broadcasting with faulty nodes

We consider broadcasting from a fault-free source to all nodes of a completely connected n-node network in the presence of k faulty nodes. Every node can communicate with at most one other node in a unit of time and during this period every pair of communicating nodes can exchange information packets. Faulty nodes cannot send information. Broadcasting is adaptive, i.e., a node schedules its next communication on the basis of information currently available to it. Assuming that the fraction of faulty nodes is bounded by a constant smaller than 1, we construct a broadcasting algorithm working in worst-case time O(log² n).