Abstract: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.
From: Shengcai Liu [view email]
[v1]
Mon, 22 Jun 2026 04:14:12 UTC (2,968 KB)
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