Graph Neural Networks with Triangle-Based Messages for the Multicut Problem

TL;DR

This paper introduces a triangle-based message passing graph neural network tailored for the multicut problem, achieving superior solution quality and speed compared to existing heuristics.

Contribution

The paper proposes a novel GNN architecture that uses triangle-based messages and edge features, specifically designed for the multicut problem.

Findings

Outperforms state-of-the-art heuristics in solution quality.

Finds optimal solutions in seconds for some instances.

Maintains feasible runtimes on synthetic and real-world data.

Abstract

The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be adapted further to its specific objective function and constraints. In this article, we introduce such an adapted graph neural network architecture in which features are assigned only to edges, and the computation of messages is based on triangles in the underlying graph. Experiments with synthetic and real-world instances with up to 200 nodes show that our method outperforms state-of-the-art heuristic solvers in terms of solution quality while maintaining feasible runtimes. For some instances, our method finds optimal solutions in seconds whereas exact solvers need hours to find and certify optimal solutions.