The pessimistic diagnosability of alternating group graphs under the PMC model

The process of identifying faulty processors is called the diagnosis of the system. Several diagnostic models have been proposed, the most popular is the PMC (Preparata, Metze and Chen) diagnostic model. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolate...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Information processing letters 2015-02, Vol.115 (2), p.151-154
1. Verfasser: Tsai, Chang-Hsiung
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 154
container_issue 2
container_start_page 151
container_title Information processing letters
container_volume 115
creator Tsai, Chang-Hsiung
description The process of identifying faulty processors is called the diagnosis of the system. Several diagnostic models have been proposed, the most popular is the PMC (Preparata, Metze and Chen) diagnostic model. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty nodes within a set containing at most one fault-free node. A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free node mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. Jwo et al. [11] introduced the alternating group graph as an interconnection network topology for computing systems. The proposed graph has many advantages over hypercubes and star graphs. For example, for all alternating group graphs, every pair of vertices in the graph are connected by a Hamiltonian path and the graph can embed cycles with arbitrary length with dilation 1. In this article, we completely determine the pessimistic diagnosability of an n-dimensional alternating group graph, denoted by AGn. Furthermore, tp(AGn)=4n−11 for n≥4. •The pessimistic diagnosability of popular interconnection networks is studied.•Alternation group graph is shown to have the strong diagnosability property.•The pessimistic diagnosability of an n-dimensional alternating group graph is determined.
doi_str_mv 10.1016/j.ipl.2014.09.003
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1628654107</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S002001901400177X</els_id><sourcerecordid>3510817581</sourcerecordid><originalsourceid>FETCH-LOGICAL-c325t-31a54a2005d55193f70bb923e326ad75a7b19d71cb68967f2d8b965e10cd5a973</originalsourceid><addsrcrecordid>eNp9kMtqwzAQRUVpoenjA7ozdG13RrJki65K6AvSxyJdC9mSExnHciW7kL-vQ7ruZmZzz-VyCLlByBBQ3LWZG7qMAuYZyAyAnZAFlgVNBaI8JQsACimghHNyEWMLACJnxYK8r7c2GWyMbufi6OrEOL3pfdSV69y4T3yT6G60odej6zfJJvhpmK8etjGZemNDMs4Fn2_LZOeN7a7IWaO7aK___iX5enpcL1_S1cfz6_JhldaM8jFlqHmuKQA3nKNkTQFVJSmzjAptCq6LCqUpsK5EKUXRUFNWUnCLUBuuZcEuye2xdwj-e7JxVK2f5pFdVChoKXiOcEjhMVUHH2OwjRqC2-mwVwjqoE21atamDtoUSDVrm5n7I2Pn-T_OBhVrZ_vaGhdsPSrj3T_0L8KydJ4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1628654107</pqid></control><display><type>article</type><title>The pessimistic diagnosability of alternating group graphs under the PMC model</title><source>ScienceDirect Journals (5 years ago - present)</source><creator>Tsai, Chang-Hsiung</creator><creatorcontrib>Tsai, Chang-Hsiung</creatorcontrib><description>The process of identifying faulty processors is called the diagnosis of the system. Several diagnostic models have been proposed, the most popular is the PMC (Preparata, Metze and Chen) diagnostic model. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty nodes within a set containing at most one fault-free node. A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free node mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. Jwo et al. [11] introduced the alternating group graph as an interconnection network topology for computing systems. The proposed graph has many advantages over hypercubes and star graphs. For example, for all alternating group graphs, every pair of vertices in the graph are connected by a Hamiltonian path and the graph can embed cycles with arbitrary length with dilation 1. In this article, we completely determine the pessimistic diagnosability of an n-dimensional alternating group graph, denoted by AGn. Furthermore, tp(AGn)=4n−11 for n≥4. •The pessimistic diagnosability of popular interconnection networks is studied.•Alternation group graph is shown to have the strong diagnosability property.•The pessimistic diagnosability of an n-dimensional alternating group graph is determined.</description><identifier>ISSN: 0020-0190</identifier><identifier>EISSN: 1872-6119</identifier><identifier>DOI: 10.1016/j.ipl.2014.09.003</identifier><identifier>CODEN: IFPLAT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Alternating group graph ; Cayley graph ; Fault diagnosis ; Geometry ; Graph theory ; Graphs ; Interconnection networks ; Mathematical analysis ; Mathematical models ; Network topologies ; Pessimistic diagnosability ; PMC model ; Studies</subject><ispartof>Information processing letters, 2015-02, Vol.115 (2), p.151-154</ispartof><rights>2014 Elsevier B.V.</rights><rights>Copyright Elsevier Sequoia S.A. Feb 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-31a54a2005d55193f70bb923e326ad75a7b19d71cb68967f2d8b965e10cd5a973</citedby><cites>FETCH-LOGICAL-c325t-31a54a2005d55193f70bb923e326ad75a7b19d71cb68967f2d8b965e10cd5a973</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ipl.2014.09.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,778,782,3539,27911,27912,45982</link.rule.ids></links><search><creatorcontrib>Tsai, Chang-Hsiung</creatorcontrib><title>The pessimistic diagnosability of alternating group graphs under the PMC model</title><title>Information processing letters</title><description>The process of identifying faulty processors is called the diagnosis of the system. Several diagnostic models have been proposed, the most popular is the PMC (Preparata, Metze and Chen) diagnostic model. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty nodes within a set containing at most one fault-free node. A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free node mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. Jwo et al. [11] introduced the alternating group graph as an interconnection network topology for computing systems. The proposed graph has many advantages over hypercubes and star graphs. For example, for all alternating group graphs, every pair of vertices in the graph are connected by a Hamiltonian path and the graph can embed cycles with arbitrary length with dilation 1. In this article, we completely determine the pessimistic diagnosability of an n-dimensional alternating group graph, denoted by AGn. Furthermore, tp(AGn)=4n−11 for n≥4. •The pessimistic diagnosability of popular interconnection networks is studied.•Alternation group graph is shown to have the strong diagnosability property.•The pessimistic diagnosability of an n-dimensional alternating group graph is determined.</description><subject>Alternating group graph</subject><subject>Cayley graph</subject><subject>Fault diagnosis</subject><subject>Geometry</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Interconnection networks</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Network topologies</subject><subject>Pessimistic diagnosability</subject><subject>PMC model</subject><subject>Studies</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kMtqwzAQRUVpoenjA7ozdG13RrJki65K6AvSxyJdC9mSExnHciW7kL-vQ7ruZmZzz-VyCLlByBBQ3LWZG7qMAuYZyAyAnZAFlgVNBaI8JQsACimghHNyEWMLACJnxYK8r7c2GWyMbufi6OrEOL3pfdSV69y4T3yT6G60odej6zfJJvhpmK8etjGZemNDMs4Fn2_LZOeN7a7IWaO7aK___iX5enpcL1_S1cfz6_JhldaM8jFlqHmuKQA3nKNkTQFVJSmzjAptCq6LCqUpsK5EKUXRUFNWUnCLUBuuZcEuye2xdwj-e7JxVK2f5pFdVChoKXiOcEjhMVUHH2OwjRqC2-mwVwjqoE21atamDtoUSDVrm5n7I2Pn-T_OBhVrZ_vaGhdsPSrj3T_0L8KydJ4</recordid><startdate>20150201</startdate><enddate>20150201</enddate><creator>Tsai, Chang-Hsiung</creator><general>Elsevier B.V</general><general>Elsevier Sequoia S.A</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20150201</creationdate><title>The pessimistic diagnosability of alternating group graphs under the PMC model</title><author>Tsai, Chang-Hsiung</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-31a54a2005d55193f70bb923e326ad75a7b19d71cb68967f2d8b965e10cd5a973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Alternating group graph</topic><topic>Cayley graph</topic><topic>Fault diagnosis</topic><topic>Geometry</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Interconnection networks</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Network topologies</topic><topic>Pessimistic diagnosability</topic><topic>PMC model</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tsai, Chang-Hsiung</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Information processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tsai, Chang-Hsiung</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The pessimistic diagnosability of alternating group graphs under the PMC model</atitle><jtitle>Information processing letters</jtitle><date>2015-02-01</date><risdate>2015</risdate><volume>115</volume><issue>2</issue><spage>151</spage><epage>154</epage><pages>151-154</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>The process of identifying faulty processors is called the diagnosis of the system. Several diagnostic models have been proposed, the most popular is the PMC (Preparata, Metze and Chen) diagnostic model. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty nodes within a set containing at most one fault-free node. A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free node mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. Jwo et al. [11] introduced the alternating group graph as an interconnection network topology for computing systems. The proposed graph has many advantages over hypercubes and star graphs. For example, for all alternating group graphs, every pair of vertices in the graph are connected by a Hamiltonian path and the graph can embed cycles with arbitrary length with dilation 1. In this article, we completely determine the pessimistic diagnosability of an n-dimensional alternating group graph, denoted by AGn. Furthermore, tp(AGn)=4n−11 for n≥4. •The pessimistic diagnosability of popular interconnection networks is studied.•Alternation group graph is shown to have the strong diagnosability property.•The pessimistic diagnosability of an n-dimensional alternating group graph is determined.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ipl.2014.09.003</doi><tpages>4</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0020-0190
ispartof Information processing letters, 2015-02, Vol.115 (2), p.151-154
issn 0020-0190
1872-6119
language eng
recordid cdi_proquest_journals_1628654107
source ScienceDirect Journals (5 years ago - present)
subjects Alternating group graph
Cayley graph
Fault diagnosis
Geometry
Graph theory
Graphs
Interconnection networks
Mathematical analysis
Mathematical models
Network topologies
Pessimistic diagnosability
PMC model
Studies
title The pessimistic diagnosability of alternating group graphs under the PMC model
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-15T22%3A32%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20pessimistic%20diagnosability%20of%20alternating%20group%20graphs%20under%20the%20PMC%20model&rft.jtitle=Information%20processing%20letters&rft.au=Tsai,%20Chang-Hsiung&rft.date=2015-02-01&rft.volume=115&rft.issue=2&rft.spage=151&rft.epage=154&rft.pages=151-154&rft.issn=0020-0190&rft.eissn=1872-6119&rft.coden=IFPLAT&rft_id=info:doi/10.1016/j.ipl.2014.09.003&rft_dat=%3Cproquest_cross%3E3510817581%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1628654107&rft_id=info:pmid/&rft_els_id=S002001901400177X&rfr_iscdi=true