A Graph Neural Network with Negative Message Passing for Graph Coloring

TL;DR

This paper introduces a novel graph neural network with negative message passing and a new loss function to effectively solve graph coloring problems, especially heterophilous types, outperforming existing algorithms.

Contribution

It presents a new GNN model with negative message passing and a specialized loss function tailored for heterophilous graph coloring problems, advancing the state-of-the-art.

Findings

Outperforms five state-of-the-art algorithms on benchmark problems

Effective in handling heterophilous graph coloring tasks

Demonstrates robustness on real-world applications

Abstract

Graph neural networks have received increased attention over the past years due to their promising ability to handle graph-structured data, which can be found in many real-world problems such as recommended systems and drug synthesis. Most existing research focuses on using graph neural networks to solve homophilous problems, but little attention has been paid to heterophily-type problems. In this paper, we propose a graph network model for graph coloring, which is a class of representative heterophilous problems. Different from the conventional graph networks, we introduce negative message passing into the proposed graph neural network for more effective information exchange in handling graph coloring problems. Moreover, a new loss function taking into account the self-information of the nodes is suggested to accelerate the learning process. Experimental studies are carried out to compare the proposed graph model with five state-of-the-art algorithms on ten publicly available graph coloring problems and one real-world application. Numerical results demonstrate the effectiveness of the proposed graph neural network.