Many structured overlay networks rely on a ring invariant as a core network connectivity element. The responsibility ranges of the participating peers and navigability principles (greedy routing) heavily depend on the ring structure. For correctness guarantees, each node needs to eagerly maintain its immediate neighboring links - the ring invariant. However, the ring maintenance is an expensive task and it may not even be possible to maintain the ring invariant continuously under high churn, particularly as the network size grows. Furthermore, routing anomalies in the network, peers behind firewalls and Network Address Translators (NATs) create non-transitivity effects, which inevitably lead to the violation of the ring invariant. We argue ...