A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in O( n/ ^2) Rounds
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We present a deterministic distributed 2-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is O( n Δ / ^2 Δ). This improves over the currently best known deterministic 2-approximation implied by [KVY94]. Our solution generalizes the (2+ϵ)-approximation algorithm of [BCS17], improving the dependency on ϵ^-1 from linear to logarithmic. In addition, for every ϵ=(Δ)^-c, where c≥ 1 is a constant, our algorithm computes a (2+ϵ)-approximation in O(Δ / Δ) rounds (which is asymptotically optimal).
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