General and efficient decentralized consensus protocols

Abstract

In this article we are interested in computing a function or a predicate whose arguments are distributed on the nodes (or processors) of a network. When the computation is finished two cases may occur according to the application. The result is either known by each node or distributed on each node. Furthermore during the computation all the nodes have the same behaviour (there is no privileged node). We shall call the distributed algorithms which achieve such computations "consensus protocols".

A general and efficient consensus protocol is presented here. It is based on the concepts of phases and filterings. This algorithm can be applied to many problems, for example to compute a minimum routing table for the nodes of the network or to find the maximum of the identities of the nodes (election). If we denote by D the diameter of the network and by m the number of channels (communication links), its message complexity is at most 2(D+1)m and its time complexity is at most (2D+1)τ, where τ is the maximum transmission delay on a channel.

This work has been done with the support of the french GRECO-PRC C³.