MinMax Algorithms for Stabilizing Consensus

TL;DR

This paper introduces a MinMax algorithm for stabilizing consensus in dynamic, anonymous networks where a root agent can influence all others over bounded periods, without global knowledge or central control.

Contribution

The paper presents a generic MinMax algorithm that achieves stabilizing consensus in highly dynamic, anonymous networks with time-varying topologies, requiring no global information.

Findings

Algorithm works with dynamic root agents

No need for global network size information

Efficient message and storage requirements

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. 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 the agents. Such topologies are highly dynamic (in particular, roots may change arbitrarily over time) and enforce no strong connectivity property (an agent may be never a root). Our distributed MinMax algorithms require neither central control (e.g., synchronous starts) nor any global information (eg.,on the size of the network), and are quite efficient in terms of message size and storage requirements.