In Peer-to-Peer networks based on consistent hashing and
ring topology, each server is responsible for an interval chosen (pseudo-)
randomly on a unit circle. The topology of the network, the communica-
tion load, and the amount of data a server stores depend heavily on the
length of its interval.

Additionally, the nodes are allowed to join the network or to leave
it at any time. Such operations can destroy the balance of the network,
even if all the intervals had equal lengths in the beginning.

This paper deals with the task of keeping such a system balanced,
so that the lengths of intervals assigned to the nodes differ at most by
a constant factor. We propose a simple fully distributed scheme, which
works in a constant number of rounds and achieves optimal balance with
high probability. Each round takes time at most O(D + log n), where D
is the diameter of a specific network (e.g. (log n) for Chord and O(log n/log log n)
for the continous-discrete approach proposed by Naor and Wieder).

The scheme is a continuous process which does not have to be informed
about the possible imbalance or the current size of the network to start
working. The total number of migrations is within a constant factor from
the number of migrations generated by the optimal centralized algorithm
starting with the same initial network state.