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