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

We present a simple deterministic distributed (2+ ǫ)-approximation algorithm for minimum weight vertex cover, which completes in O(log∆/ǫ log log∆) rounds, where ∆ is the maximum degree in the graph, for any ǫ > 0 which is at most O(1). For a constant ǫ, this implies a constant approximation in O(log∆/ log log∆) rounds, which contradicts the lower bound of [KMW10]. ∗Technion, Department of Computer Science, [email protected], [email protected], [email protected]. Supported in part by the Israel Science Foundation (grant 1696/14).