Rearranging trees for robust consensus

TL;DR

This paper investigates the robustness of consensus algorithms on trees by using the H2 norm, providing a way to order and rearrange trees to enhance their noise resilience.

Contribution

It introduces a systematic method to order undirected trees by robustness and proposes a decentralized approach to improve robustness through tree rearrangement.

Findings

Derived a partial ordering of undirected trees based on H2 norm

Provided a constructive method for ordering directed trees

Suggested a decentralized tree rearrangement strategy to enhance robustness

Abstract

In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees according to the H2 norm. Our approach for undirected trees provides a constructive method for deriving an ordering for directed trees. Further, our approach suggests a decentralized manner in which trees can be rearranged in order to improve their robustness.