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We present a deterministic distributed $2$-approximation algorithm for theMinimum Weight Vertex Cover problem in the CONGEST model whose round complexityis $O(\log n \log \Delta / \log^2 \log \Delta)$. This improves over thecurrently best known deterministic 2-approximation implied by [KVY94]. Oursolution generalizes the $(2+\epsilon)$-approximation algorithm of [BCS17],improving the dependency on $\epsilon^{-1}$ from linear to logarithmic. Inaddition, for every $\epsilon=(\log \Delta)^{-c}$, where $c\geq 1$ is aconstant, our algorithm computes a $(2+\epsilon)$-approximation in $O(\log\Delta / \log \log \Delta)$~rounds (which is asymptotically optimal).

A Deterministic Distributed $2$-Approximation for Weighted Vertex Cover in $O(\log n\log\Delta / \log^2\log\Delta)$ Rounds