Can I find stable matchings in complex networks?
Extending Stable and Popular Matching Algorithms from Bipartite to Arbitrary Instances
This paper addresses the challenge of finding optimal or near-optimal solutions in scenarios where agents have preferences over potential partners, extending classic matching algorithms to more complex cases relevant to multi-agent AI. It proposes a novel approach for finding stable matchings in "roommate" problems, a generalization where any two agents can be matched, not just pairs from distinct sets.
The key point relevant to LLM-based multi-agent systems is the introduction of "popular fractional-matchings", allowing for nuanced collaborations where agents can divide their engagement (like attention or resources) between multiple partners. This concept mirrors and enhances techniques for managing interactions and collaborations within multi-agent LLM systems, leading to more robust and flexible agent coordination.