Graph partitioning aims to divide a graph into $k$ disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature. As a result, conventional approximation algorithms rely on heuristic methods, sometimes with approximation guarantees and sometimes without. Unfortunately, traditional approaches are tailored for specific partitioning objectives and do not generalize well across other known partitioning objectives from the literature. To overcome this limitation, and learn heuristics from the data directly, neural approaches have emerged, demonstrating promising outcomes. In this study, we extend this line of work through a novel framework, NeuroCut. NeuroCut introduces two key innovations over prevailing methodologies. First, it is inductive to both graph topology and the partition count, which is provided at query time. Second, by leveraging a reinforcement learning based framework over node representations derived from a graph neural network, NeuroCut can accommodate any optimization objective, even those encompassing non-differentiable functions. Through empirical evaluation, we demonstrate that NeuroCut excels in identifying high-quality partitions, showcases strong generalization across a wide spectrum of partitioning objectives, and exhibits resilience to topological modifications.

通过一种新框架，NeuroCut，结合了神经网络和强化学习，并具有对不可微分函数的优化能力，从而在图分区问题中表现出色，并在多种分区目标中展现出较强的泛化能力和拓扑鲁棒性。

NeuroCUT: 面向鲁棒图分割的神经方法