Finding Consensus in Multi-Agent Networks Using Heat Kernel Pagerank

TL;DR

This paper introduces an efficient heat kernel pagerank-based algorithm for computing consensus in large multi-agent networks, achieving sublinear runtime and balancing accuracy with performance.

Contribution

It proposes a novel, scalable consensus algorithm using heat kernel pagerank, suitable for very large networks, with theoretical performance guarantees.

Findings

Runs in sublinear time relative to network size

Provides quantitative tradeoff analysis between accuracy and efficiency

Applicable to both weighted average and leader-following consensus

Abstract

We present a new and efficient algorithm for determining a consensus value for a network of agents. Different from existing algorithms, our algorithm evaluates the consensus value for very large networks using heat kernel pagerank. We consider two frameworks for the consensus problem, a weighted average consensus among all agents, and consensus in a leader-following formation. Using a heat kernel pagerank approximation, we give consensus algorithms that run in time sublinear in the size of the network, and provide quantitative analysis of the tradeoff between performance guarantees and error estimates.