Learning-Augmented Algorithms for Online Vertex Cover

2026-06-22

AI Summary

This work introduces learning-augmented algorithms to the online weighted vertex cover problem under irrevocable decision constraints, presenting deterministic and randomized approaches tailored respectively for bipartite and general graphs. By incorporating a tunable parameter λ, the proposed algorithms achieve optimal trade-offs between consistency and robustness: for bipartite graphs, they attain robustness 1/(1−e⁻λ) and consistency λ/(1−e⁻λ); for general graphs, robustness (1+1/λ) and consistency (1+λ). Both bounds are proven to be theoretically tight. Notably, this trade-off mirrors that of the classical ski rental problem. Empirical evaluations on both synthetic and real-world datasets confirm the practical efficacy of the proposed methods.

Abstract

This 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.

Problem

• online vertex cover
• learning-augmented algorithms
• advice
• robustness-consistency tradeoff
• weighted graphs

Innovation

• learning-augmented algorithms
• online vertex cover
• robustness-consistency tradeoff
• bipartite graphs
• advice-based prediction