Graph partitioning aims to divide a graph into disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature. Conventional methods, like approximation algorithms or heuristics, are designed for distinct partitioning objectives and fail to achieve generalization across other important partitioning objectives. Recently machine learning-based methods have been developed that learn directly from data. Further, these methods have a distinct advantage of utilizing node features that carry additional information. However, these methods assume differentiability of target partitioning objective functions and cannot generalize for an unknown number of partitions, i.e., they assume the number of partitions is provided in advance. In this study, we develop NeuroCUT with two key innovations over previous methodologies. First, by leveraging a reinforcement learning-based framework over node representations derived from a graph neural network and positional features, NeuroCUT can accommodate any optimization objective, even those with non-differentiable functions. Second, we decouple the parameter space and the partition count making NeuroCUT inductive to any unseen number of partition, which is provided at query time. 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 strong generalization to unseen partition count.

翻译：图划分旨在将图划分为不相交的子集，同时优化特定的划分目标。由于其组合性质，大多数与图划分相关的公式化问题都表现出NP难特性。传统方法（如近似算法或启发式方法）针对不同的划分目标设计，无法在其他重要划分目标上实现泛化。近年来，基于机器学习的方法被开发出来，可直接从数据中学习。此外，这些方法具有利用携带额外信息的节点特征的独特优势。然而，这些方法假设目标划分目标函数可微，并且无法泛化到未知数量的划分，即它们假设划分数量是预先提供的。在本研究中，我们开发了NeuroCUT，相较于先前方法具有两个关键创新。首先，通过利用基于强化学习的框架，该框架作用于从图神经网络和位置特征导出的节点表示，NeuroCUT能够适应任何优化目标，即使是那些具有不可微函数的目标。其次，我们将参数空间与划分数量解耦，使得NeuroCUT能够归纳适用于任何未见过的划分数量，该数量在查询时提供。通过实证评估，我们证明NeuroCUT在识别高质量划分方面表现出色，在广泛的划分目标谱系中展现出强大的泛化能力，并对未见过的划分数量表现出强大的泛化性。