A nearly optimal upper bound for the self-stabilization time in Herman's algorithm

Feng, Y; Zhang, L

A nearly optimal upper bound for the self-stabilization time in Herman's algorithm

Feng, Y

Zhang, L

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Publication Type:: Conference Proceeding
Citation:: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2014, 8704 LNCS pp. 342 - 356
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Feng, Y https://orcid.org/0000-0002-3097-3896	en_US
dc.contributor.author	Zhang, L	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2014, 8704 LNCS pp. 342 - 356	en_US
dc.identifier.isbn	9783662445839	en_US
dc.identifier.issn	0302-9743	en_US
dc.identifier.uri	http://hdl.handle.net/10453/33131
dc.description.abstract	Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Herman's self-stabilization algorithm and study its expected self-stabilization time. McIver and Morgan have conjectured the optimal upper bound being 0.148N 2, where N denotes the number of processors. We present an elementary proof showing a bound of 0.167N2, a sharp improvement compared with the best known bound 0.521N2. Our proof is inspired by McIver and Morgan's approach: we find a nearly optimal closed form of the expected stabilization time for any initial configuration, and apply the Lagrange multipliers method to give an upper bound of it. © 2014 Springer-Verlag.	en_US
dc.relation.ispartof	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en_US
dc.relation.isbasedon	10.1007/978-3-662-44584-6_24	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	A nearly optimal upper bound for the self-stabilization time in Herman's algorithm	en_US
dc.type	Conference Proceeding
utslib.citation.volume	8704 LNCS	en_US
utslib.for	080203 Computational Logic and Formal Languages	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	8704 LNCS	en_US

Abstract:

Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Herman's self-stabilization algorithm and study its expected self-stabilization time. McIver and Morgan have conjectured the optimal upper bound being 0.148N 2, where N denotes the number of processors. We present an elementary proof showing a bound of 0.167N2, a sharp improvement compared with the best known bound 0.521N2. Our proof is inspired by McIver and Morgan's approach: we find a nearly optimal closed form of the expected stabilization time for any initial configuration, and apply the Lagrange multipliers method to give an upper bound of it. © 2014 Springer-Verlag.

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