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We present a simple deterministic distributed $(2+\epsilon)$-approximationalgorithm for minimum weight vertex cover, which completes in$O(\log{\Delta}/\epsilon\log\log{\Delta})$ rounds, where $\Delta$ is themaximum degree in the graph, for any $\epsilon>0$ which is at most $O(1)$. Fora constant $\epsilon$, this implies a constant approximation in$O(\log{\Delta}/\log\log{\Delta})$ rounds, which contradicts the lower bound of[KMW10].

A Distributed $(2+\epsilon)$-Approximation for Vertex Cover in $O(\log{\Delta}/\epsilon\log\log{\Delta})$ Rounds