Consensus with Ternary Messages

TL;DR

This paper introduces a protocol for real-valued average consensus in networks where agents exchange only ternary messages, ensuring polynomial convergence time without global topology knowledge.

Contribution

The paper presents a novel consensus protocol using only ternary messages that guarantees convergence on time-varying graphs with minimal local information.

Findings

Protocol achieves polynomial convergence time

Works on time-varying undirected graphs

Requires only local degree bounds

Abstract

We provide a protocol for real-valued average consensus by networks of agents which exchange only a single message from the ternary alphabet {-1,0,1} between neighbors at each step. Our protocol works on time-varying undirected graphs subject to a connectivity condition, has a worst-case convergence time which is polynomial in the number of agents and the initial values, and requires no global knowledge about the graph topologies on the part of each node to implement except for knowing an upper bound on the degrees of its neighbors.