Learning-Augmented Algorithms for Online Vertex Cover

This paper studies learning-augmented online weighted vertex cover with advice and a parameter $\lambda \in (0,1)$. We consider two graph cases: 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 $\frac{1}{1-e^{-\lambda }}$-robust and $\frac{\lambda }{1-e^{-\lambda }}$-consistent. For the general graph model, we give a deterministic algorithm that is $(1+\frac{1}{\lambda })$-robust and $(1+\lambda )$-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.