Finding Consensus in Multi-Agent Networks Using Heat Kernel Pagerank

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.