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arXiv · 2606.22831

Learning-Augmented Algorithms for Online Vertex Cover

Tianhang Lu·Runtian Ren·Shengcai Liu
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Abstract

This paper studies learning-augmented online weighted vertex cover with local advice and a tradeoff parameter $λ\in (0,1)$. 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 $\frac{1}{1-e^{-λ}}$-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.

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Tianhang Lu, Runtian Ren, Shengcai Liu. 2026-07-30. Learning-Augmented Algorithms for Online Vertex Cover. https://arxiv.org/abs/2606.22831

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