  Overlay networks, where nodes communicate with neighbors over logical links
consisting of zero or more physical links, have become an important part of
modern networking. From data centers to IoT devices, overlay networks are used
to organize a diverse set of processes for efficient operations like searching
and routing. Many of these overlay networks operate in fragile environments
where faults that perturb the logical network topology are commonplace.
Self-stabilizing overlay networks offer one approach for managing these faults,
promising to build or restore a particular topology from any weakly-connected
initial configuration.
  Designing efficient self-stabilizing algorithms for many topologies, however,
is not an easy task. For non-trivial topologies that have desirable properties
like low diameter and robust routing in the face of node or link failures,
self-stabilizing algorithms to date have had at least linear running time or
space requirements. In this work, we address this issue by presenting an
algorithm for building a Chord network that has polylogarithmic time and space
complexity. Furthermore, we discuss how the technique we use for building this
Chord network can be generalized into a ``design pattern'' for other desirable
overlay network topologies.
