面向最大独立集的双图神经网络多级粗化
Dual-GNN Multilevel Coarsening for Maximum Independent Set
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中文总结 AI 辅助
提出学习型图边稀疏化方法GES，利用几何与组合优化信息自适应剪枝，在MATILDA和TSPLIB上剪除95%以上边且解差距小于1%。
中文摘要 AI 辅助
精确求解大规模旅行商问题（TSP）计算代价高昂。研究者常采用图稀疏化方法来提高计算效率。传统稀疏化方法通常依赖固定启发式规则，未能充分利用实例特有的结构信息。本文提出图边稀疏化（GES），一种面向欧几里得TSP的基于学习的稀疏化方法。通过融合几何结构信息与组合优化技术，所提方法针对不同实例自适应生成稀疏化图，显著减小图规模并加速求解过程。实验结果表明，在MATILDA数据集上，该方法可剪除高达95%的边，同时解与最优值的差距保持在1%以内。此外，该方法在TSPLIB上展现出强泛化能力，在部分大规模实例中，剪枝率超过99%，而最优性差距仍低于1%。
英文摘要
The maximum independent set (MIS) problem is a fundamental NP-hard combinatorial optimization problem with applications in scheduling, resource allocation, and network analysis. Exact solvers can provide high-quality solutions or optimality certificates, but their computational cost grows rapidly with graph size, while hand-crafted heuristics improve scalability at the expense of guarantees. Learning-based methods offer an alternative by exploiting structural patterns across graph instances, yet directly predicting independent sets can make global coordination difficult on large graphs. We instead use learning to guide multilevel graph coarsening while retaining combinatorial search for final decision making. Our Dual-GNN Multilevel Coarsening framework uses a Partition GNN to score candidate contractions and a Representative GNN to select top-k local independent-set states for each final cluster. Experiments on Erdős--Rényi graphs with up to 2,000 vertices demonstrate a favorable quality--runtime trade-off. On 500-vertex instances with certified optima, our method achieves an average independent-set size of 19.20, corresponding to 99.5\% of the optimal value of 19.30, while reducing the mean wall-clock time from 643.57 seconds for exact solving to 3.41 seconds, yielding an approximately 189$\times$ speedup. On larger graphs with 1,000 and 2,000 vertices, our method achieves the best mean solution quality among all evaluated methods. Moreover, although trained only on Erdős--Rényi graphs with edge probability $p=0.35$, the learned coarsening policy generalizes effectively across both unseen graph densities and structurally different graph families.
发表机构
- Lanzhou University（兰州大学）
机构由 AI 辅助整理，请以论文原文为准。
