Fast and Simple Densest Subgraph with Predictions

TL;DR

This paper introduces learning-augmented algorithms for the NP-hard densest subgraph problem, leveraging predictors to achieve near-optimal solutions efficiently and demonstrating their effectiveness on real-world data.

Contribution

It proposes simple linear-time algorithms that incorporate node prediction to approximate the densest at-most-$k$ subgraph problem.

Findings

Algorithms achieve a (1-ε) approximation with accurate predictors.

Experimental results show effectiveness on real-world graphs.

Methods are simple and run in linear time.

Abstract

We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the solution (e.g., a machine learning classifier), one can design simple linear-time algorithms that achieve a $(1-\epsilon)$approximation. Finally, we present experimental results demonstrating the effectiveness of our methods for the densest at-most-$k$ subgraph problem on real-world graphs.