An end-to-end bi-objective approach to deep graph partitioning

Graphs are ubiquitous in real-world applications, such as computation graphs and social networks. Partitioning large graphs into smaller, balanced partitions is often essential, with the bi-objective graph partitioning problem aiming to minimize both the “cut” across partitions and the imbalance in partition sizes. However, existing heuristic methods face scalability challenges or overlook partition balance, leading to suboptimal results. Recent deep learning approaches, while promising, typically focus only on node-level features and lack a truly end-to-end framework, resulting in limited performance. In this paper, we introduce a novel method based on graph neural networks (GNNs) that leverages multilevel graph features and addresses the problem end-to-end through a bi-objective formulation. Our approach explores node-, local-, and global-level features, and introduces a well-bounded bi-objective function that minimizes the cut while ensuring partition-wise balance across all partitions. Additionally, we propose a GNN-based deep model incorporating a $Hardmax$ operator, allowing the model to optimize partitions in a fully end-to-end manner. Experimental results on 12 datasets across various applications and scales demonstrate that our method significantly improves both partitioning quality and scalability compared to existing bi-objective and deep graph partitioning baselines.