Fast and Simple Densest Subgraph with Predictions

We study the densest subgraph problem and its variants through the lens of learning-augmented algorithms. For this problem, the greedy algorithm by Charikar (APPROX 2000) provides a linear-time $1/2$-approximation, while computing the exact solution typically requires solving a linear program or performing maximum flowthis http URLshow that given a partial solution, i.e., one produced by a machine learning classifier that captures at least a $(1 - \epsilon)$-fraction of nodes in the optimal subgraph, it is possible to design an extremely simple linear-time algorithm that achieves a provable $(1 - \epsilon)$-approximation. Our approach also naturally extends to the directed densest subgraph problem and several NP-hardthis http URLexperiment on the Twitch Ego Nets dataset shows that our learning-augmented algorithm outperforms Charikar's greedy algorithm and a baseline that directly returns the predicted densest subgraph without additional algorithmic processing.

@article{bui2025_2505.12600,
  title={ Fast and Simple Densest Subgraph with Predictions },
  author={ Thai Bui and Hoa T. Vu },
  journal={arXiv preprint arXiv:2505.12600},
  year={ 2025 }
}