A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in O(\log N\log \varDelta /\log ^2\log \varDelta ) Rounds.

We present a deterministic distributed 2-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is (O(log nlog varDelta / log ^2log varDelta )). This improves over the currently best known deterministic 2-approximation implied by [KVY94]. Our solution generalizes the ((2+epsilon ))-approximation algorithm of [BCS17], improving the dependency on (epsilon ^{-1}) from linear to logarithmic. In addition, for every (epsilon =(log varDelta )^{-c}), where (cge 1) is a constant, our algorithm computes a (left( 2+epsilon right) )-approximation in (O(log {varDelta }/log log {varDelta })) rounds (which is asymptotically optimal).