Cayley Graph Optimization for Scalable Multi-Agent Communication Topologies

2026-04-07

AI Summary

This work addresses the challenge of designing scalable and efficient communication topologies for large-scale multi-agent systems, where fully connected graphs incur prohibitive complexity and existing sparse topologies rely on handcrafted designs that struggle to balance scalability with effective information propagation. The authors propose CayleyTopo, a method that treats the communication graph as an optimizable variable and employs lightweight reinforcement learning to optimize the generating set of circulant Cayley graphs, minimizing graph diameter to accelerate worst-case information dissemination. By integrating number-theoretic priors with a message-propagation scoring mechanism, CayleyTopo efficiently navigates an enormous search space to discover richly structured topologies approaching the Moore bound. Experiments demonstrate that CayleyTopo outperforms existing hand-designed topologies in terms of propagation speed, link robustness, and communication overhead, offering a scalable foundation for efficient multi-agent coordination.

Technology Category

• Multiagent Systems: Agent Communication
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Large-scale multi-agent communication has long faced a scalability bottleneck: fully connected networks require quadratic complexity, yet existing sparse topologies rely on hand-crafted rules. This paper treats the communication graph itself as a design variable and proposes CayleyTopo, a family of circulant Cayley graphs whose generator sets are optimized to minimize diameter, directly targeting worst-case information propagation speed. To navigate the enormous search space of possible generator sets, we develop a lightweight reinforcement learning framework that injects a number-theoretic prior to favor structurally rich generators, alongside a message-propagation score that provides dense connectivity feedback during construction. The resulting CayleyTopo consistently outperforms existing hand-crafted topologies, achieving faster information dissemination, greater resilience to link failures, and lower communication load, all while approaching the theoretical Moore bound. Our study opens the door to scalable, robust, and efficient communication foundations for future multi-agent systems, where the graph itself becomes optimizable rather than a fixed constraint.

Problem

• scalability
• multi-agent communication
• Cayley graphs
• communication topology
• information propagation

Innovation

• Cayley graph
• multi-agent communication
• topology optimization
• reinforcement learning
• scalability