Learning-Augmented Algorithms for Online Steiner Tree

TL;DR

This paper introduces learning-augmented algorithms for the online Steiner tree problem, leveraging machine-learned predictions to improve performance and gracefully degrade with prediction errors in both directed and undirected graphs.

Contribution

It develops new online algorithms that incorporate predictions for terminal arrivals, achieving better competitive ratios and robustness against prediction inaccuracies.

Findings

Algorithms outperform traditional bounds with accurate predictions.

Performance remains strong even with modest prediction accuracy.

Theoretical results align with empirical performance on distribution-based graphs.

Abstract

This paper considers the recently popular beyond-worst-case algorithm analysis model which integrates machine-learned predictions with online algorithm design. We consider the online Steiner tree problem in this model for both directed and undirected graphs. Steiner tree is known to have strong lower bounds in the online setting and any algorithm's worst-case guarantee is far from desirable. This paper considers algorithms that predict which terminal arrives online. The predictions may be incorrect and the algorithms' performance is parameterized by the number of incorrectly predicted terminals. These guarantees ensure that algorithms break through the online lower bounds with good predictions and the competitive ratio gracefully degrades as the prediction error grows. We then observe that the theory is predictive of what will occur empirically. We show on graphs where terminals are drawn from a distribution, the new online algorithms have strong performance even with modestly correct predictions.