The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied NP-hard combinatorial problem with several real-world applications. As such, a number of greedy heuristics have been suggested that strike a good balance between coloring quality, execution time, and also parallel scalability. In this work, we introduce a graph neural network (GNN) based ordering heuristic and demonstrate that it outperforms existing greedy ordering heuristics both on quality and performance. Previous results have demonstrated that GNNs can produce high-quality colorings but at the expense of excessive running time. The current paper is the first that brings the execution time down to compete with existing greedy heuristics. Our GNN model is trained using both supervised and unsupervised techniques. The experimental results show that a 2-layer GNN model can achieve execution times between the largest degree first (LF) and smallest degree last (SL) ordering heuristics while outperforming both on coloring quality. Increasing the number of layers improves the coloring quality further, and it is only at four layers that SL becomes faster than the GNN. Finally, our GNN-based coloring heuristic achieves superior scaling in the parallel setting compared to both SL and LF.

本文解决了图着色问题，这是一种在无向图中为顶点分配不同颜色的NP难题。提出了一种基于图神经网络的排序启发式，显著提升了着色质量和执行效率。研究表明，在平行处理能力上，GNN模型在质量和性能上超越了现有的贪心排序启发式方法。

将图神经网络作为平行图着色的排序启发式