  We present and analyze a simple and general scheme to build a churn
(fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to
"convert" a static network into a dynamic distributed hash table(DHT)-based P2P
network such that all the good properties of the static network are guaranteed
with high probability (w.h.p). Applying our scheme to a cube-connected cycles
network, for example, yields a $O(\log N)$ degree connected network, in which
every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages,
where $N$ is the expected stable network size. Our scheme has an constant
storage overhead (the number of nodes responsible for servicing a data item)
and an $O(\log N)$ overhead (messages and time) per insertion and essentially
no overhead for deletions. All these bounds are essentially optimal. While DHT
schemes with similar guarantees are already known in the literature, this work
is new in the following aspects:
  (1) It presents a rigorous mathematical analysis of the scheme under a
general stochastic model of churn and shows the above guarantees;
  (2) The theoretical analysis is complemented by a simulation-based analysis
that validates the asymptotic bounds even in moderately sized networks and also
studies performance under changing stable network size;
  (3) The presented scheme seems especially suitable for maintaining dynamic
structures under churn efficiently. In particular, we show that a spanning tree
of low diameter can be efficiently maintained in constant time and logarithmic
number of messages per insertion or deletion w.h.p.
  Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic
Analysis.
