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

We present a deterministic distributed 2-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGESTmodel whose round complexity isO(log n log∆/ log log∆). This improves over the currently best known deterministic 2-approximation implied by [KVY94]. Our solution generalizes the (2 + ǫ)-approximation algorithm of [BCS17], improving the dependency on ǫ from linear to logarithmic. In addition, for every ǫ = (log∆), where c ≥ 1 is a constant, our algorithm computes a (2 + ǫ)-approximation in O(log∆/ log log∆) rounds (which is asymptotically optimal). Technion, Department of Computer Science, [email protected]. This work was partially sponsored by the Technion-HPI reseach school. Tel Aviv University, [email protected]. NII, Japan, [email protected], [email protected] . This work was supported by JST ERATO Grant Number JPMJER1201, Japan.