Fault-tolerance and lookup consistency are considered crucial properties for building applications on top of structured overlay networks. Many of these networks use the ring topology for the organization or their peers. The network must handle multiple joins, leaves and failures of peers while keeping the connection between every pair of successor-predecessor correct. This property makes the maintenance of the ring very costly and temporarily impossible to achieve, requiring periodic stabilization for fixing the ring. We introduce the relaxed-ring topology that does not rely on a perfect successor-predecessor relationship and it does not need a any periodic maintenance. Leaves and failures are considered as the same type of event providing a fault-tolerant and self-organizing maintenance of the ring. Relaxed-ring's limitations with respect to failure handling are formally identified, providing strong guarantees to develop applications on top of the architecture. Besides permanent failures, the paper analyses temporary failures and false suspicions caused by broken links, which are often ignored.
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