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We investigate the maintenance of overlay networks under massive churn, i.e.nodes joining and leaving the network. We assume an adversary that may churn aconstant fraction $\alpha n$ of nodes over the course of $\mathcal{O}(\log n)$rounds. In particular, the adversary has an almost up-to-date information ofthe network topology as it can observe an only slightly outdated topology thatis at least $2$ rounds old. Other than that, we only have the provably minimalrestriction that new nodes can only join the network via nodes that have takenpart in the network for at least one round.  Our contributions are as follows: First, we show that it is impossible tomaintain a connected topology if adversary has up-to-date information about thenodes' connections. Further, we show that our restriction concerning the joinis also necessary. As our main result present an algorithm that constructs anew overlay -- completely independent of all previous overlays -- every $2$rounds. Furthermore, each node sends and receives only $\mathcal{O}(\log^3 n)$messages each round. As part of our solution we propose the Linearized DeBruijnSwarm (LDS), a highly churn resistant overlay, which will be maintained by thealgorithm. However, our approaches can be transferred to a variety of classicalP2P Topologies where nodes are mapped into the $[0,1)$-interval.

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