Efficient Randomised Broadcasting in Random Regular Networks with Applications in Peer-to-Peer Systems

We consider broadcasting in random d-regular graphs by using a simple modification of the so-called random phone call model introduced by Karp et al. [19]. In the phone call model every time step each node calls on a randomly chosen neighbour to establish a, communication channel with this node. The communication channels can then be used to transmit; messages in both directions. We show that, if we allow every node to choose four distinct neighbours instead of one, then the average number of message transmissions per node decreases exponentially. Formally, we present a broadcasting algorithm that, has time complexity O(log n) and uses O(n log log n) transmission,, per message. In contrast, we show for the standard model that every distributed and address-oblivious algorithm that broadcasts a message in time O(log n.) needs Omega(n log n/log d) message transmission. Our algorithm can efficiently handle limited communication failures, only requires, rough estimates of the number of nodes, and is robust against limited changes in the size of the network. Our results have applications in peer-to-peer networks and replicated databases.