אלגוריתמים מלמדים לפתרון קבוצה עם גודל משונה

תקציר מקורי באנגליתarXiv:2606.22831v2 Announce Type: replace-cross Abstract: This paper studies learning-augmented online weighted vertex cover with local advice and a tradeoff parameter $\lambda \in (0,1)$. 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 $\frac{1}{1-e^{-\lambda}}$-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 op