Our main result is designing an algorithm that returns a vertex cover of $\mathcal{G}^\star$ with size at most $(3/2+\epsilon)$ times the expected size of the minimum vertex cover, using only $O(n/\epsilon p)$ non-adaptive queries. This improves over the best-known 2-approximation algorithm by Behnezhad, Blum, and Derakhshan [SODA'22], who also show that $\Omega(n/p)$ queries are necessary to achieve any constant approximation. Our guarantees also extend to instances where edge realizations are not fully independent. We complement this upper bound with a tight $3/2$-approximation lower bound for stochastic graphs whose edges realizations demonstrate mild correlations.

翻译：我们的主要成果是设计了一种算法，该算法使用仅$O(n/\epsilon p)$次非自适应查询，返回一个$\mathcal{G}^\star$的顶点覆盖，其大小最多为最小顶点覆盖期望大小的$(3/2+\epsilon)$倍。这改进了Behnezhad、Blum和Derakhshan [SODA'22]目前已知的最优2近似算法，他们同时证明了实现任何常数近似都需要$\Omega(n/p)$次查询。我们的保证还适用于边实现不完全独立的实例。我们为这一上界补充了一个紧致的$3/2$近似下界，该下界适用于边实现呈现轻微相关性的随机图。