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  "path": "/abs/2606.22831v1",
  "publishedAt": "2026-06-23T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Tianhang Lu",
    "Runtian Ren",
    "Shengcai Liu"
  ],
  "textContent": "**Authors:** Tianhang Lu, Runtian Ren, Shengcai Liu\n\nThis paper studies learning-augmented online weighted vertex cover with advice and a parameter $λ\\in (0,1)$. 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 $\\frac{1}{1-e^{-λ}}$-robust and $\\fracλ{1-e^{-λ}}$-consistent. For the general graph model, we give a deterministic algorithm that is $(1+\\frac{1}λ)$-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.",
  "title": "Learning-Augmented Algorithms for Online Vertex Cover"
}