Abstract
AbstractLet N be a network of asynchronous processors, viewed as vertices, communicating by sending messages over unreliable unidirectional edges, and let r be a specified vertex in N. We consider the problem of constructing efficient and reliable protocols to broadcast messages from r to all other vertices of N: Suppose that for some vertex v in N, at least k edges must be deleted in order to disconnect v from r; we say that a protocol PR, this message will eventually reach v. A protocol is faithful if it is reliable fro all vertices of the network. A general lower bound on the message complexity of faithful protocols, which is at most linear in the network size, is given. It is also shown that this bound can always be achieved by protocols which use the local memories of the vertices to record messages. On the other hand, it is shown that for certain networks, all faithful protocols that use no memory for local computations have a message complexity which is exponential in the network sixe. A characterization of networks that hve faithful protocosl with optimal message and space complexities is also given.
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