MinMax algorithms for stabilizing consensus

Abstract

In the stabilizing consensus problem each agent of a networked system has an input value and is repeatedly writing an output value; it is required that eventually all the output values stabilize to the same value which, moreover, must be one of the input values. We study this problem for a synchronous model with identical and anonymous agents that are connected by a time-varying topology and may join the system at any time (asynchronous start). Our main result is a generic MinMax algorithm that solves the stabilizing consensus problem in this model when, in each sufficiently long but bounded period of time, there is an agent, called a root, that can send messages, possibly indirectly, to all other agents. We stress that the bound on the time required for achieving this rootedness property is unknown to the agents. Such topologies are highly dynamic (in particular, roots may change arbitrarily over time) and may have very weak connectivity properties (an agent may be never a root). Our distributed MinMax algorithms thus require neither central control nor any global information and are also quite efficient in terms of message size and storage requirements.