We study the densest subgraph problem and its variants through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the densest subgraph (e.g., a machine-learning classifier), one can design simple and practical linear-time algorithms that achieve a $(1-ε)$-approximation to the densest subgraph. Our approach also extends to the NP-Hard densest at-most-$k$ subgraph problem and to the directed densest subgraph variant. Finally, we present experimental results demonstrating the effectiveness of our methods.

翻译：本研究通过增强学习算法的视角，探讨稠密子图问题及其变体。我们证明，在给定能够合理预测节点是否属于最稠密子图的预测器（例如机器学习分类器）的情况下，可以设计出简单实用的线性时间算法，实现对最稠密子图的$(1-ε)$近似求解。该方法还可扩展至NP难的最多$k$节点稠密子图问题以及有向稠密子图变体。最后，我们通过实验验证了所提方法的有效性。