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MA-GTS: A Multi-Agent Framework for Solving Complex Graph Problems in Real-World Applications

Zike Yuan, Ming Liu, Hui Wang, Bing Qin

TL;DR

This work addresses the challenge of solving complex, real-world graph problems embedded in noisy, long-form text. It introduces MA-GTS, a three-layer multi-agent framework (IEL, KIL, AEL) that maps unstructured data to structured graphs, dynamically selects algorithms, and delivers interpretable reasoning. The authors validate MA-GTS on the novel G-REAL dataset, showing superior efficiency, accuracy, and scalability over state-of-the-art LLMs and multi-agent baselines, including substantial improvements on large TSP instances. The approach offers practical impact by enabling robust, cost-effective graph reasoning in logistics, networks, and planning domains, with strong generalization to both complex and simpler graph tasks.

Abstract

Graph-theoretic problems arise in real-world applications like logistics, communication networks, and traffic optimization. These problems are often complex, noisy, and irregular, posing challenges for traditional algorithms. Large language models (LLMs) offer potential solutions but face challenges, including limited accuracy and input length constraints. To address these challenges, we propose MA-GTS (Multi-Agent Graph Theory Solver), a multi-agent framework that decomposes these complex problems through agent collaboration. MA-GTS maps the implicitly expressed text-based graph data into clear, structured graph representations and dynamically selects the most suitable algorithm based on problem constraints and graph structure scale. This approach ensures that the solution process remains efficient and the resulting reasoning path is interpretable. We validate MA-GTS using the G-REAL dataset, a real-world-inspired graph theory dataset we created. Experimental results show that MA-GTS outperforms state-of-the-art approaches in terms of efficiency, accuracy, and scalability, with strong results across multiple benchmarks (G-REAL 94.2%, GraCoRe 96.9%, NLGraph 98.4%).MA-GTS is open-sourced at https://github.com/ZIKEYUAN/MA-GTS.git.

MA-GTS: A Multi-Agent Framework for Solving Complex Graph Problems in Real-World Applications

TL;DR

This work addresses the challenge of solving complex, real-world graph problems embedded in noisy, long-form text. It introduces MA-GTS, a three-layer multi-agent framework (IEL, KIL, AEL) that maps unstructured data to structured graphs, dynamically selects algorithms, and delivers interpretable reasoning. The authors validate MA-GTS on the novel G-REAL dataset, showing superior efficiency, accuracy, and scalability over state-of-the-art LLMs and multi-agent baselines, including substantial improvements on large TSP instances. The approach offers practical impact by enabling robust, cost-effective graph reasoning in logistics, networks, and planning domains, with strong generalization to both complex and simpler graph tasks.

Abstract

Graph-theoretic problems arise in real-world applications like logistics, communication networks, and traffic optimization. These problems are often complex, noisy, and irregular, posing challenges for traditional algorithms. Large language models (LLMs) offer potential solutions but face challenges, including limited accuracy and input length constraints. To address these challenges, we propose MA-GTS (Multi-Agent Graph Theory Solver), a multi-agent framework that decomposes these complex problems through agent collaboration. MA-GTS maps the implicitly expressed text-based graph data into clear, structured graph representations and dynamically selects the most suitable algorithm based on problem constraints and graph structure scale. This approach ensures that the solution process remains efficient and the resulting reasoning path is interpretable. We validate MA-GTS using the G-REAL dataset, a real-world-inspired graph theory dataset we created. Experimental results show that MA-GTS outperforms state-of-the-art approaches in terms of efficiency, accuracy, and scalability, with strong results across multiple benchmarks (G-REAL 94.2%, GraCoRe 96.9%, NLGraph 98.4%).MA-GTS is open-sourced at https://github.com/ZIKEYUAN/MA-GTS.git.

Paper Structure

This paper contains 32 sections, 3 equations, 16 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. MA-GTS
  4. Information Extraction Layer (IEL)
  5. Knowledge Integration Layer (KIL)
  6. Algorithm Execution Layer (AEL)
  7. G-REAL
  8. Data Collection
  9. Data Statistics
  10. Evaluation
  11. Experiments Setup
  12. Datasets
  13. Baselines and Foundation Model
  14. Results and Analysis
  15. Performance on real-world problems
  16. ...and 17 more sections

Figures (16)

  • Figure 1: MA-GTS leverages multi-agent collaboration to overcome noise and semantic loss in real-world graph problems, leading to better answers.
  • Figure 2: MA-GTS framework for solving real-world graph problems, consisting of three layers: Information Extraction, Knowledge Integration, and Algorithm Execution, each with specialized agents.
  • Figure 3: This figure details the G-REAL dataset's composition and features, along with the full MA-GTS graph problem-solving pipeline, outlining each component's functions and input/output formats.
  • Figure 4: Performance of different problems across varying node numbers (MA-GTS v.s. o3-mini).
  • Figure 5: Details of Graph Theory Knowledge Base
  • ...and 11 more figures