Avatar: A Time- and Space-Efficient Self-Stabilizing Overlay Network

TL;DR

This paper introduces a novel self-stabilizing overlay network algorithm based on binary search trees that efficiently stabilizes in expected polylogarithmic time with minimal degree increase, improving fault tolerance in dynamic environments.

Contribution

It presents the first self-stabilizing overlay network algorithm that is both time-efficient and maintains low node degree during stabilization.

Findings

Expected stabilization time is polylogarithmic.

Node degree increases only polylogarithmically during stabilization.

The algorithm is randomized and locally checkable.

Abstract

Overlay networks present an interesting challenge for fault-tolerant 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. \emph{Self-stabilizing overlay networks} promise that, starting from any weakly-connected configuration, 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 configuration. In this paper, we present the first self-stabilizing overlay network algorithm that does not incur this penalty. Specifically, 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 \emph{and} increases a node's degree by only a polylogarithmic factor in expectation.