The maintenance of efficient and robust overlay networks is one of the most fundamental and reoccurring themes in networking. This paper presents a survey of state-of-the-art algorithms to design and repair overlay networks in a distributed manner. In particular, we discuss basic algorithmic primitives to preserve connectivity, review algorithms for the fundamental problem of graph linearization, and then survey self-stabilizing algorithms for metric and scalable topologies. We also identify open problems and avenues for future research.

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