A Tiny Graph Neural Network for Inverse Graph Partitioning with Imbalance Constraints.

Recent years have witnessed an interest in inverse graph partitioning (IGP), which stems from many real-world applications such as anti-community detection and detention room allocation. Previous studies typically focus on the balanced IGP problem that divides a graph into multiple subgraphs of the same size. However, many practical scenarios require partitioning a graph into subgraphs of different sizes, which limits the feasibility of existing IGP methods. In this paper, we present an end-to-end model to solve IGP with imbalance constraints, called IIGPN, which utilizes a tiny graph neural network to learn subgraph assignments for nodes. IIGPN is iteratively trained against an unsupervised loss function that encodes the imbalanced IGP problem. Empirical experiments show that IIGPN significantly outperforms existing algorithms and approximates the optimal solution on large-scale graphs. Moreover, IIGPN reduces the computation time by about 90 percent compared to the best heuristic algorithm.