A Solution to Fastest Distributed Consensus Problem for Generic Star & K-cored Star Networks

TL;DR

This paper derives optimal weights and convergence rates for distributed average consensus in star and K-cored star networks, demonstrating faster convergence with the new topology and weight optimization.

Contribution

It provides closed-form formulas for optimal weights and convergence rates in star and K-cored star networks, improving consensus speed.

Findings

Optimal weights significantly enhance convergence speed.

K-cored star topology outperforms traditional star topology.

Simulations confirm the effectiveness of the proposed methods.

Abstract

Distributed average consensus is the main mechanism in algorithms for decentralized computation. In distributed average consensus algorithm each node has an initial state, and the goal is to compute the average of these initial states in every node. To accomplish this task, each node updates its state by a weighted average of its own and neighbors' states, by using local communication between neighboring nodes. In the networks with fixed topology, convergence rate of distributed average consensus algorithm depends on the choice of weights. This paper studies the weight optimization problem in distributed average consensus algorithm. The network topology considered here is a star network where the branches have different lengths. Closed-form formulas of optimal weights and convergence rate of algorithm are determined in terms of the network's topological parameters. Furthermore generic K-cored star topology has been introduced as an alternative to star topology. The introduced topology benefits from faster convergence rate compared to star topology. By simulation better performance of optimal weights compared to other common weighting methods has been proved.