Stochastic Minimum Vertex Cover in General Graphs: a 3/2-Approximation
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Our main result is designing an algorithm that returns a vertex cover of 𝒢^⋆ with size at most (3/2+ϵ) times the expected size of the minimum vertex cover, using only O(n/ϵ p) non-adaptive queries. This improves over the best-known 2-approximation algorithm by Behnezhad, Blum, and Derakhshan [SODA'22], who also show that Ω(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.
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