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

TL;DR

GraphDC introduces a hierarchical divide-and-conquer multi-agent framework that decomposes large graphs into smaller parts for scalable and robust reasoning on graph algorithms, outperforming existing methods.

Contribution

Proposes a novel multi-agent divide-and-conquer framework for scalable graph reasoning, reducing complexity and improving performance on large graph instances.

Findings

GraphDC outperforms existing methods on diverse graph reasoning tasks.

Hierarchical decomposition improves robustness on large graphs.

The framework scales effectively to larger graph instances.

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. 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. 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.