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 can receive information but cannot send it. Broadcasting is adaptive, i.e. a node schedules its next communication on the basis of information currently available to it. We study worst case running time of fault-tolerant broadcasting algorithms in two models: in the wake-up model only nodes already having the source message can call other nodes and in the unrestricted model all fault-free nodes can call. In the rst model we give an optimal algorithm working in time k +dlog(n?k)e. In the second model we give an algorithm working in time O(log 2 n), whenever the fraction of faulty nodes is bounded by a constant smaller than 1.