The Agent Coordination Bound (ACB): A Framework for Multi-LLM Fleet Sizing, Topology Selection, and Deployment Diagnostics

Key Points

• The aim is to provide a principled criterion for determining optimal fleet sizes in multi-agent LLM frameworks.
• Introduced the Agent Coordination Bound (ACB) as a structural heuristic.
• Derived a formula for predicting optimal fleet size: n* = ⌈a/c⌉.
• Explored properties like degradation probability and communication channel growth in coordination.
• Developed a topology crossover theorem and Coordination Bottleneck Index (CBI) for diagnostics.
• Predicted the optimal fleet size where coordination overhead outweighs reasoning gain.
• Defined a degradation probability indicating performance risk as fleet size increases.
• Established a Coordinated Bottleneck Index (CBI) as a practical tool for deployment diagnostics.

Abstract