Broadcast in the Rendezvous Model

Abstract

In many large, distributed or mobile networks, broadcast algorithms are used to update information stored at the nodes. In this paper, we propose a new model of communication based on rendezvous and analyze a multi-hop distributed algorithm to broadcast a message in a synchronous setting. In the rendezvous model, two neighbors u and v can communicate if and only if u calls v and v calls u simultaneously. Thus nodes u and v obtain a rendezvous at a meeting point. If m is the number of meeting points, the network can be modeled by a graph of n vertices and m edges. At each round, every vertex chooses a random neighbor and there is a rendezvous if an edge has been chosen by its two extremities. Rendezvous enable an exchange of information between the two entities. We get sharp lower and upper bounds on the time complexity in terms of number of rounds to broadcast: we show that, for any graph, the expected number of rounds is between log n and O(n ²). For these two bounds, we prove that there exist some graphs for which the expected number of rounds is either O(log n) or Ω(n ²). For specific topologies, additional bounds are given.