Ditributed Broadcast in Radio Networks OF Unknown Topology

A multi-hop synchronous radio network is said to be unknown if the nodes have no knowledge of the topology. A basic task in radio network is that of broadcasting a message (created by a fixed source node) to all nodes of the network. Typical operations in real-life radio networks is the multi-broadcast that consists in performing a set of r independent broadcasts. The study of broadcast operations on unknown radio network is started by the seminal paper of Bar-Yehuda et al. [J. Comput. System Sci. 45 (1992) 104] and has been the subject of several recent works. In this paper, we study the completion and the termination time of distributed protocols for both the (single) broadcast and the multi-broadcast operations on unknown networks as functions of the number of nodes n, the maximum eccentricity D, the maximum in-degree Δ, and the congestion c of the networks. We establish new connections between these operations and some combinatorial concepts, such as selective families, strongly selective families (also known as superimposed codes), and pairwise r-different families. Such connections, combined with a set of new lower and upper bounds on the size of the above families, allow us to derive new lower bounds and new distributed protocols for the broadcast and multi-broadcast operations. In particular, our upper bounds are almost tight and strongly improve over the previous bounds for a large class of networks.