Randomized Broadcasting in Radio Networks, 1992;

The paper investigates deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multi-hop synchronous radio networks. The model consists of an arbitrary (undirected) network, with processors communicating in synchronous time-slots subject to the following rules. In each time-slot, each processor acts either as a transmitter or as a receiver. A processor acting as a receiver is said to receive a message in that time-slot t if exactly one of its neighbors transmits in that time-slot. The message received is the one transmitted. If more than one neighbor transmits in that timeslot, a conflict occurs. In this case the receiver may either get a message from one of the transmitting neighbors or get no message. It is assumed that conflicts (or “collisions”) are not detected, hence a processor cannot distinguish the case in which no neighbor transmits from the case in which one or more of its neighbors transmits during that time-slot. The processors are not required to have ID’s nor do they know their neighbors, in particular the processors do not know the topology of the network. The only inputs required by the protocol are the number of processors in the network – n, ∆ – an a priori known upper bound on the maximum degree in the network and the error bound – 2. (All bounds are a priori known to the algorithm.) Broadcast is a task initiated by a single processor, called the source, transmitting a single message. The goal is to have the message reach all processors in the network.