An Analysis Framework for Distributed Hierarchical Directories

We provide a novel analysis framework for distributed hierarchical directories for an arbitrary set of dynamic (online) requests. We prove a general ${\cal O}(\eta\cdot \varphi \cdot \sigma^3 \cdot h)$ competitive ratio for any distributed hierarchical directory, where η is a write set size related...

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Bibliographic Details
Published inDistributed Computing and Networking Vol. 7730; pp. 378 - 392
Main Authors Sharma, Gokarna, Busch, Costas
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2013
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Competitive Ratio
Hamiltonian Path
Leader Node
Online Algorithm
Transactional Memory
Online AccessGet full text
ISBN9783642356674
3642356672
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-35668-1_26

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Summary:We provide a novel analysis framework for distributed hierarchical directories for an arbitrary set of dynamic (online) requests. We prove a general ${\cal O}(\eta\cdot \varphi \cdot \sigma^3 \cdot h)$ competitive ratio for any distributed hierarchical directory, where η is a write set size related parameter, ϕ and σ are stretch and growth related parameters, and h is the number of levels in the hierarchy. Through this framework, we give bounds for several known distributed directory protocols. In general network topologies, we obtain ${\cal O}(\log^2 n\cdot\log D)$ competitive ratio, where n and D are the number of nodes and the diameter, respectively, of the network. Moreover, we obtain ${\cal O}(\log D)$ competitive ratio in constant-doubling metric topologies. To the best of our knowledge, this is the first (competitive) dynamic analysis for distributed hierarchical directories.
Bibliography:Original Abstract: We provide a novel analysis framework for distributed hierarchical directories for an arbitrary set of dynamic (online) requests. We prove a general \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal O}(\eta\cdot \varphi \cdot \sigma^3 \cdot h)$\end{document} competitive ratio for any distributed hierarchical directory, where η is a write set size related parameter, ϕ and σ are stretch and growth related parameters, and h is the number of levels in the hierarchy. Through this framework, we give bounds for several known distributed directory protocols. In general network topologies, we obtain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal O}(\log^2 n\cdot\log D)$\end{document} competitive ratio, where n and D are the number of nodes and the diameter, respectively, of the network. Moreover, we obtain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal O}(\log D)$\end{document} competitive ratio in constant-doubling metric topologies. To the best of our knowledge, this is the first (competitive) dynamic analysis for distributed hierarchical directories.
ISBN:9783642356674
3642356672
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-35668-1_26