Graph Neural Networks as Ordering Heuristics for Parallel Graph Coloring

TL;DR

This paper introduces a GNN-based heuristic for graph coloring that outperforms traditional greedy heuristics in both coloring quality and parallel scalability, while maintaining competitive execution times.

Contribution

It presents the first GNN-based graph coloring heuristic that balances high-quality solutions with efficient execution times suitable for parallel processing.

Findings

GNN heuristic outperforms greedy heuristics in coloring quality.

Execution times of the GNN are competitive with traditional heuristics.

GNN scaling improves with more layers, especially in parallel settings.

Abstract

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.