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O(log n)-time Overlay Network Construction from Graphs with Out-degree 1

Summary: O(log n)-time Overlay Network Construction
from Graphs with Out-degree 1
James Aspnes
Yinghua Wu
July 15, 2007
A fast self-stabilizing algorithm is described to rapidly construct a balanced overlay network
from a directed graph initially with out-degree 1, a natural starting case that arises in peer-
to-peer 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 double-headed 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, self-stabilizing,


Source: Aspnes, James - Department of Computer Science, Yale University


Collections: Computer Technologies and Information Sciences