On Efficient Gossiping in Radio Networks

A communication network is very often modelled as a graph of connections in which the nodes exchange information (messages) via (un)directed links. An associated communication protocol determines the way the messages are exchanged. Among the most popular network models are: (1) the

message passing model

in which a node in one round can inform all its neighbours; (2) the

telephone model

also known as the

matching model

where in each round edges along which the exchange of messages is performed form a matching in the graph of connections. More recently, due to arrival of wireless technology (3) the

radio network model

attracted more attention in algorithms community. In this model, a message transmitted by a node is destined for all neighbours of this node. It is assumed, however, that due to interference a node can successfully receive a message if and only if exactly one of its neighbours transmits during this round.

The two most fundamental problems in relation to information dissemination are:

broadcasting

(one-to-all communication) and

gossiping

(total information exchange). In broadcasting, the goal is to distribute a piece of information (

broadcast message

) from a distinguished source node to all other nodes in the network. In gossiping, however, each node in the network is expected to distribute its own message to every other node in the network. A lot of attention has been given to the broadcasting problem that resulted in a large volume of efficient algorithmic solutions in the models described above. However, much less is known about gossiping. The latter problem is more complex algorithmically (in principle it is a simultaneous multiple-source broadcasting) thus it concerns more advanced communication strategies. Further study on efficient gossiping methods gained recently an extra motivation through an increasing interest in, e.g.,

information aggregation

methods that propel fundamental applications in sensor networks. Also when the use of randomisation is permitted gossiping provides an interesting context for a distributed version of the

coupon collector problem

.

This paper is a short survey on the most important developments in efficient radio gossiping. We discuss deterministic as well as randomized methods of communication in the context of a variety of models taking into account knowledge in relation to the network size and topology, orientation of connections and the upper bound on the size of messages. Using this opportunity we also shed more light on several combinatorial structures and algorithmic solutions that emerged during studies on efficient radio broadcasting and gossiping.