Broadcasting with a Bounded Fraction of Faulty Nodes

We consider the problem of broadcasting a message from one processor (called the source) tonother processors. We adopt the 1-port half-duplex model in which every processor (node) can communicate with at most one other node in a unit of time and during this period one of the communicating nodes can only send information and the other can only receive it. The source is fault-free but all other nodes are subject to permanent failures. A faulty node can receive the message but cannot relay it. The fraction of faulty nodes is bounded by a constant. We consider nonadaptive broadcasting algorithms working correctly in the presence of faulty nodes and investigate their worst-case running time. We also show lower bounds for broadcasting time under this scenario. Our main result is the construction of a fault-tolerant broadcasting algorithm whose running time is less than 1.73 times larger than optimal, for sufficiently largen.