Learning-Augmented Algorithms for Online Vertex Cover

This paper studies learning-augmented online weighted vertex cover with local advice and a tradeoff parameter λ ∈ (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 frac11-e-λ-robust and fracλ1-e-λ-consistent. For the general graph model, we give a deterministic algorithm that is (1+frac1λ)-robust and (1+λ)-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.