 
Summary: O(log n)time Overlay Network Construction
from Graphs with Outdegree 1
James Aspnes
Yinghua Wu
July 15, 2007
Abstract
A fast selfstabilizing algorithm is described to rapidly construct a balanced overlay network
from a directed graph initially with outdegree 1, a natural starting case that arises in peer
topeer systems where each node attempts to join by contacting some single other node. This
algorithm constructs a balanced search tree in time O(W + log n), where W is the key length
and n is the number of nodes, improving by a factor of log n on the previous bound starting from
a general graph, while retaining the properties of low contention and short messages. Our con
struction includes an improved version of the distributed Patricia tree structure of Angluin et
al. [2], which we call a doubleheaded radix tree. This data structure responds gracefully to
node failures and supports search, predecessor, and successor operations in O(W) time with
smoothly distributed load for predecessor and successor operations. Though the resulting tree
data structure is highly vulnerable to disconnection due to failures, the fast predecessor and
successor operations (as shown in previous work) can be used to quickly construct standard
overlay networks with more redundancy.
Keywords: Overlay network, balanced search tree, pipeline, randomization, selfstabilizing,
