Fastest Distributed Consensus on Path Network

TL;DR

This paper presents an analytical solution for the fastest distributed consensus problem on path networks, using semidefinite programming to derive optimal weights and improve efficiency over previous numerical methods.

Contribution

It provides the first closed-form analytical solution for FDC on path networks, advancing beyond prior numerical approaches.

Findings

Derived the optimal weights analytically for path networks.

Validated the solution through semidefinite programming techniques.

Achieved faster consensus compared to existing methods.

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. Most of the methods proposed so far deal with the FDC averaging algorithm problem by numerical convex optimization methods and in general no closed-form solution for finding FDC has been offered up to now except in [3] where the conjectured answer for path has been proved. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for the Path network using semidefinite programming particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions.