Perfect Broadcasting in Unlabeled Networks

We consider broadcasting a message from one node to all other nodes of an asynchronous totally unlabeled network: neither nodes nor links of the network have a priori assigned labels but they know the topology of the network. Nodes can send messages of arbitrary size and we are interested in minimizing the total number of messages. Broadcasting in an n-node unlabeled network is perfect if it uses n?1 messages (the minimum even in the labeled network). We show that the problem of deciding whether an arbitrary network admits perfect broadcasting from a given source, is NP-hard. We characterize regular networks in which perfect broadcasting from every node is possible, and give such broadcasting algorithms.