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

2026-05-13

AI Summary

This work addresses the NP-hard Multicut problem, which finds broad applications in bioinformatics, data mining, and computer vision, by proposing a specialized graph neural network architecture. The method models features exclusively on edges and introduces, for the first time, a message-passing mechanism that leverages triangular structures inherent in the input graph to align with the objective function and constraints of the Multicut problem. Experimental results demonstrate that the proposed approach outperforms state-of-the-art heuristic solvers in solution quality on both synthetic and real-world instances with up to 200 nodes. Notably, it obtains optimal solutions within seconds on certain instances where exact solvers require several hours.

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.

Problem

• multicut problem
• combinatorial optimization
• graph neural networks
• NP-hard
• triangle-based messages

Innovation

• Graph Neural Networks
• Triangle-based Messages
• Multicut Problem
• Combinatorial Optimization
• Message Passing