The impact of knowledge on broadcasting time in radio networks

Abstract

We consider the problem of distributed deterministic broadcasting in radio networks. Nodes send messages in synchronous time-slots. Each node v has a given transmission range. All nodes located within this range can receive messages from v. However, a node situated in the range of two or more nodes that send messages simultaneously, cannot receive these messages and hears only noise. Each node knows only its own position and range, as well as the maximum of all ranges. Broadcasting is adaptive: Nodes can decide on the action to take on the basis of previously received messages, silence or noise. We prove a lower bound on broadcasting time in this model and construct a broadcasting protocol whose performance matches this bound for the simplest case when nodes are situated on a line and the network has constant depth. We also show that if nodes do not even know their own range, every broadcasting protocol must be hopelessly slow. While distributed randomized broadcasting algorithms, and, on the other hand, deterministic off-line broadcasting algorithms assuming full knowledge of the radio network, have been extensively studied in the literature, ours are the first results concerning broadcasting algorithms that are distributed and deterministic at the same time.We show that in this case the amount of knowledge available to nodes influences the efficiency of broadcasting in a significant way.