Avatar: A Time- and Space-E cient Self-Stabilizing Overlay Network

Overlay networks present an interesting challenge for faulttolerant computing. Many overlay networks operate in dynamic environments (e.g. the Internet), where faults are frequent and widespread, and the number of processes in a system may be quite large. Recently, self-stabilizing overlay networks have been presented as a method for managing this complexity. Self-stabilizing overlay networks promise that, starting from any weakly-connected con guration, a correct overlay network will eventually be built. To date, this guarantee has come at a cost: nodes may either have high degree during the algorithm's execution, or the algorithm may take a long time to reach a legal con guration. In this paper, we present the rst self-stabilizing overlay network algorithm that does not incur this penalty. Speci cally, we (i) present a new locally-checkable overlay network based upon a binary search tree, and (ii) provide a randomized algorithm for self-stabilization that terminates in an expected polylogarithmic number of rounds and increases a node's degree by only a polylogarithmic factor in expectation.