Optimal Network Topology for Effective Collective Response

TL;DR

This paper investigates how the topology of interaction networks affects the collective response of multi-agent systems, revealing that optimal connectivity depends on the frequency of the external signal and is crucial for designing effective distributed systems.

Contribution

It introduces a detailed analysis of the relationship between network topology and collective response in multi-agent systems, supported by both theoretical models and robotic experiments.

Findings

Optimal interaction number decreases with signal frequency.

Response is independent of system size for large systems.

Dynamic rewiring of networks enhances collective response.

Abstract

Natural, social, and artificial multi-agent systems usually operate in dynamic environments, where the ability to respond to changing circumstances is a crucial feature. An effective collective response requires suitable information transfer among agents, and thus is critically dependent on the agents' interaction network. In order to investigate the influence of the network topology on collective response, we consider an archetypal model of distributed decision-making---the leader-follower linear consensus---and study the collective capacity of the system to follow a dynamic driving signal (the "leader") for a range of topologies and system sizes. The analysis reveals a nontrivial relationship between optimal topology and frequency of the driving signal. Interestingly, the response is optimal when each individual interacts with a certain number of agents which decreases monotonically with the frequency and, for large enough systems, is independent of the size of the system. This phenomenology is investigated in experiments of collective motion using a swarm of land robots. The emergent collective response to both a slow- and a fast-changing leader is measured and analyzed for a range of interaction topologies. These results have far-reaching practical implications for the design and understanding of distributed systems, since they highlight that a dynamic rewiring of the interaction network is paramount to the effective collective operations of multi-agent systems at different time-scales.