Maintaining balanced trees for structured distributed streaming systems

In this paper, we propose and analyze a simple local algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwarding the data to its children. Such systems are subject to a high churn, peers frequen...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 232; pp. 176 - 188
Main Authors: Giroire, F., Modrzejewski, R., Nisse, N., Pérennes, S.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 11.12.2017
Elsevier BV
Elsevier
Subjects:
Algorithms
Balanced trees
Children
Computer Science
Convergence
Data Structures and Algorithms
Diffusion
Distributed live streaming system
Graph algorithm
Peer-to-peer
Peers
Repair
Peer-to-peer
Distributed live streaming system
Balanced trees
Graph algorithm
Distributed Live Streaming System
Graph Algorithm
Balanced Trees
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:In this paper, we propose and analyze a simple local algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwarding the data to its children. Such systems are subject to a high churn, peers frequently joining and leaving the system. It is thus crucial to be able to repair the diffusion tree to allow an efficient data distribution. In particular, due to bandwidth limitations, an efficient diffusion tree must ensure that node degrees are bounded. Moreover, to minimize the delay of the streaming, the depth of the diffusion tree must also be controlled. We propose here a simple distributed repair algorithm in which each node carries out local operations based on its degree and on the subtree sizes of its children. In a synchronous setting, we first prove that starting from any n-node tree our process converges to a balanced binary tree in O(n2) rounds. We then describe a more restrictive model, adding a small extra information to each node, under which we adapt our algorithm to converge in Θ(nlogn) rounds.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2017.07.006