Fastest Distributed Consensus Problem on Fusion of Two Star Networks

TL;DR

This paper derives an analytical solution for the fastest distributed consensus problem on a network formed by fusing two symmetric star networks sharing a central node, using stratification and SDP techniques.

Contribution

It introduces a novel analytical method for optimal weight determination in fused star networks for distributed consensus, combining stratification and SDP.

Findings

Optimal weights are derived analytically for fused star networks.

Trade-offs between branch length and number are analyzed through simulations.

The method improves understanding of consensus speed in complex network topologies.

Abstract

Finding optimal weights for the problem of Fastest Distributed Consensus on networks with different topologies has been an active area of research for a number of years. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for a network formed from fusion of two different symmetric star networks or in other words a network consists of two different symmetric star networks which share the same central node. The solution procedure consists of stratification of associated connectivity graph of network and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Some numerical simulations are carried out to investigate the trade-off between the parameters of two fused star networks, namely the length and number of branches.