Weight Optimization for Distributed Average Consensus Algorithm in Symmetric, CCS & KCS Star Networks

TL;DR

This paper optimizes weights for distributed consensus algorithms in symmetric star networks, introduces new topologies with faster convergence, and verifies optimality through simulations under quantization constraints.

Contribution

It derives optimal weights and convergence rates for symmetric star networks and proposes two new topologies with improved convergence performance.

Findings

Optimal weights are independent of branch structure.

New CCS and KCS topologies converge faster.

Simulation confirms robustness under quantization.

Abstract

This paper addresses weight optimization problem in distributed consensus averaging algorithm over networks with symmetric star topology. We have determined optimal weights and convergence rate of the network in terms of its topological parameters. In addition, two alternative topologies with more rapid convergence rates have been introduced. The new topologies are Complete-Cored Symmetric (CCS) star and K-Cored Symmetric (KCS) star topologies. It has been shown that the optimal weights for the edges of central part in symmetric and CCS star configurations are independent of their branches. By simulation optimality of obtained weights under quantization constraints have been verified.