GraphDC: A Divide-and-Conquer Multi-Agent System for Scalable Graph Algorithm Reasoning

GraphDC：一种用于可扩展图算法推理的分治多智能体系统

Abstract: Large Language Models (LLMs) have demonstrated strong potential for many mathematical problems. However, their performance on graph algorithmic tasks is still unsatisfying, since graphs are naturally more complex in topology and often require systematic multi-step reasoning, especially on larger graphs. 摘要： 大语言模型（LLMs）在许多数学问题上展现出了强大的潜力。然而，它们在图算法任务上的表现仍不尽如人意，因为图在拓扑结构上天生更为复杂，且通常需要系统性的多步推理，尤其是在处理大规模图时更是如此。

Motivated by this gap, we propose GraphDC, a Divide-and-Conquer multi-agent framework for scalable graph algorithm reasoning. Specifically, inspired by Divide-and-Conquer design, GraphDC decomposes an input graph into smaller subgraphs, assigns each subgraph to a specialized agent for local reasoning, and uses a master agent to integrate the local outputs with inter-subgraph information to produce the final solution. 受此差距的启发，我们提出了 GraphDC，这是一个用于可扩展图算法推理的分治（Divide-and-Conquer）多智能体框架。具体而言，受分治设计思想的启发，GraphDC 将输入图分解为较小的子图，将每个子图分配给专门的智能体进行局部推理，并利用一个主智能体将局部输出与子图间的关联信息进行整合，从而得出最终解决方案。

This hierarchical design reduces the reasoning burden on individual agents, alleviates computational bottlenecks, and improves robustness on large graph instances. Extensive experiments show that GraphDC consistently outperforms existing methods on graph algorithm reasoning across diverse tasks and scales, especially on larger instances where direct end-to-end reasoning is less reliable. 这种分层设计降低了单个智能体的推理负担，缓解了计算瓶颈，并提高了在大规模图实例上的鲁棒性。大量实验表明，GraphDC 在各种任务和规模的图算法推理中始终优于现有方法，特别是在直接端到端推理可靠性较低的大规模实例上表现尤为突出。