Learning-Augmented Algorithms for Online Steiner Tree

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.

Contract Scheduling with Predictions

“…There are several recent works that study algorithms with machine-learned predictions in a status of uncertainty. Examples include online rent-or-buy problems with multiple expert predictions (Gollapudi & Panigrahi, 2019), queuing systems with job service times predicted by an oracle (Mitzenmacher, 2020), online algorithms for metrical task systems (Antoniadis, Coester, Elias, Polak, & Simon, 2020), online makespan scheduling (Lattanzi, Lavastida, Moseley, & Vassilvitskii, 2020), graph exploration (Eberle, Lindermayr, Megow, Nölke, & Schlöter, 2022) and the Steiner tree problem (Xu & Moseley, 2022), to mention only some representative results. See also the survey (Mitzenmacher & Vassilvitskii, 2020).…”

Hiring Secretaries over Time: The Benefit of Concurrent Employment

“…Naor et al [36] studied a further variant of the problem where also vertices have costs. Xu and Moseley [43] gave a learning-augmented algorithm that uses a prediction about which terminals will be added eventually. When only deletions are allowed, Gupta and Kumar [25] showed how to maintain a constant approximation while changing a constant number of edges per deletion.…”

NODLINK: An Online System for Fine-Grained APT Attack Detection and Investigation

“…The last challenge is that the current approximation algorithms for STP are still not efficient enough for APT attack detection. Existing approaches [51], [99], [77], [34] require finding the shortest path between two nodes, which is too expensive for online APT attack detection. To solve this problem, we develop an importance-oriented greedy algorithm for online STP optimization that achieves low computing complexity with a bounded competitive ratio.…”