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

Permalink

Publication Type:: Journal Article
Citation:: Distributed Computing, 2015, 28 (4), pp. 233 - 244
Issue Date:: 2015-08-04

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Accepted Manuscript VersionAdobe PDF (293.85 kB)

View on publisher's site

View statistics

Full metadata record

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	2015-08-04	en_US
dc.identifier.citation	Distributed Computing, 2015, 28 (4), pp. 233 - 244	en_US
dc.identifier.issn	0178-2770	en_US
dc.identifier.uri	http://hdl.handle.net/10453/41865
dc.description.abstract	© 2015, Springer-Verlag Berlin Heidelberg. 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 termination time. McIver and Morgan have conjectured the optimal upper bound being 0.148N2, where $$N$$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.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP130102764
dc.relation.ispartof	Distributed Computing	en_US
dc.relation.isbasedon	10.1007/s00446-015-0241-z	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	A nearly optimal upper bound for the self-stabilization time in Herman’s algorithm	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	28	en_US
utslib.for	0805 Distributed Computing	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.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	28	en_US

Abstract:

© 2015, Springer-Verlag Berlin Heidelberg. 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 termination time. McIver and Morgan have conjectured the optimal upper bound being 0.148N2, where $$N$$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.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/41865