AbstractWe consider the problem of disseminating messages in networks. We are interested in information dissemination algorithms in which machines operate independently without any knowledge of the network topology or size. Three communication tasks of increasing difficulty are studied. In blind broadcasting (BB), the goal is to communicate the source message to all nodes. In acknowledged blind broadcasting (ABB), the goal is to achieve BB and inform the source about it. Finally, in full synchronization (FS), all nodes must simultaneously enter the state terminated after receiving the source message. The algorithms should be efficient both in terms of the time required and the communication overhead they put on the network. We limit the latter by allowing every node to send a message to at most one neighbor in each round. We show that BB is achieved in time at most 2n in any n‐node network and show networks in which time 2n − o(n) is needed. For ABB, we show algorithms working in time (2 + ϵ)n, for any fixed positive constant ϵ and sufficiently large n. Thus, for both BB and ABB, our algorithms are close to optimal. Finally, we show a simple algorithm for FS working in time 3n and a more complicated algorithm which works in time 2.9n. The optimal time of full synchronization remains an open problem. © 2001 John Wiley & Sons, Inc.