 
Summary: O(log n)time Overlay Network Construction
from Graphs with Outdegree 1
James Aspnes1
and Yinghua Wu1
Yale University Department of Computer Science,
51 Prospect St, New Haven CT 06511, USA.
aspnes@cs.yale.edu, y.wu@yale.edu
Abstract. A fast selfstabilizing algorithm is described to rapidly con
struct a balanced overlay network from a directed graph initially with
outdegree 1, a natural starting case that arises in peertopeer 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 construction includes an improved version of the distributed Pa
tricia tree structure of Angluin et al. [1], 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.
