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...
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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 |
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•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> |
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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 |
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