Learning-Augmented Algorithms for Online Vertex Cover

Abstract

This paper studies learning-augmented online weighted vertex cover with local advice and a tradeoff parameter $\hat{I}»\in (0,1)$. We consider two graph settings: bipartite graphs and general graphs. In both settings, the online algorithm must maintain a feasible vertex cover under irrevocable decisions. We show that these problems admit the same robustness--consistency tradeoffs as learning-augmented ski rental. For the bipartite graph model, we give a randomized algorithm that is $\frac{1}{1-e^{-\hat{I}»}}$-robust and $\frac{\hat{I}}{»}1-e^{-\hat{I}»}$-consistent. For the general graph model, we give a deterministic algorithm that is $(1+\frac{1}{\hat{I}}»)$-robust and $(1+\hat{I}»)$-consistent. We prove that the tradeoffs above are optimal in both settings. We also validate the proposed algorithms through experiments on synthetic and real-world datasets.