Fastest Distributed Consensus on Petal Networks

TL;DR

This paper derives an analytical solution for the fastest distributed consensus averaging algorithm specifically for symmetric and CCS Petal networks, using stratification and semi-definite programming techniques.

Contribution

It introduces a novel analytical method for optimizing consensus algorithms on Petal networks, leveraging convexity and polynomial comparison techniques.

Findings

Optimal weights for symmetric Petal networks derived.

Analytical solutions for CCS Petal networks provided.

Method reveals limitations with certain leaf configurations.

Abstract

Providing an analytical solution for the problem of finding Fastest Distributed Consensus (FDC) is one of the challenging problems in the field of sensor networks. Here in this work we present analytical solution for the problem of fastest distributed consensus averaging algorithm by means of stratification and semi-definite programming, for two particular types of Petal networks, namely symmetric and Complete Cored Symmetric (CCS) Petal networks. Our method in this paper is based on convexity of fastest distributed consensus averaging problem, and inductive comparing of the characteristic polynomials initiated by slackness conditions in order to find the optimal weights. Also certain types of leaves are introduced along with their optimal weights which are not achievable by the method used in this work if these leaves are considered individually.