The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks
A set of the spanning trees in a graph G is called independent spanning trees if they have a common root r and for each vertex v\in V(G)\setminus \{r\} , the paths from v to r in any two trees are directed edge-disjoint and internally vertex-disjoint. The construction of independent spannin...
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| creator | Yang, Yi-Cheng Kao, Shih-Shun Klasing, Ralf Hsieh, Sun-Yuan Chou, Hsin-Hung Chang, Jou-Ming |
| description | A set of the spanning trees in a graph G is called independent spanning trees if they have a common root r and for each vertex v\in V(G)\setminus \{r\} , the paths from v to r in any two trees are directed edge-disjoint and internally vertex-disjoint. The construction of independent spanning trees has many practical applications in reliable communication networks, such as fault-tolerant transmission and secure message distribution. A burnt pancake network BP_{n} is a kind of Cayley graph, which has been proposed as the topology of an interconnection network. In this paper, we provide a two stages construction scheme that can be used to construct a maximal number of independent spanning trees on a burnt pancake network in O(N\times n) time, where N is the number of nodes of BP_{n} and n is the dimension of the network. Furthermore, we prove the correctness of our proposed algorithm in constructing independent spanning trees. |
| doi_str_mv | 10.1109/ACCESS.2021.3049290 |
| format | Article |
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The construction of independent spanning trees has many practical applications in reliable communication networks, such as fault-tolerant transmission and secure message distribution. A burnt pancake network <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> is a kind of Cayley graph, which has been proposed as the topology of an interconnection network. In this paper, we provide a two stages construction scheme that can be used to construct a maximal number of independent spanning trees on a burnt pancake network in <inline-formula> <tex-math notation="LaTeX">O(N\times n) </tex-math></inline-formula> time, where <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> is the number of nodes of <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the dimension of the network. Furthermore, we prove the correctness of our proposed algorithm in constructing independent spanning trees.]]></description><identifier>ISSN: 2169-3536</identifier><identifier>EISSN: 2169-3536</identifier><identifier>DOI: 10.1109/ACCESS.2021.3049290</identifier><identifier>CODEN: IAECCG</identifier><language>eng</language><publisher>Piscataway: IEEE</publisher><subject>Algorithms ; burnt pancake network ; Communication networks ; Computer Science ; Fault tolerance ; Fault tolerant systems ; fault-tolerant transmission ; Graph theory ; Independent spanning trees ; interconnection networks ; Networking and Internet Architecture ; Program processors ; Roads ; secure message distribution ; Topology ; Trees (mathematics) ; Vegetation</subject><ispartof>IEEE access, 2021, Vol.9, p.16679-16691</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c442t-4ee9afddd695d1c632b550af42ff0a1c7b4ead127231db951037b6a8273573043</citedby><cites>FETCH-LOGICAL-c442t-4ee9afddd695d1c632b550af42ff0a1c7b4ead127231db951037b6a8273573043</cites><orcidid>0000-0001-7695-3535 ; 0000-0002-9542-7968 ; 0000-0003-1627-9598 ; 0000-0003-4746-3179</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9314008$$EHTML$$P50$$Gieee$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,860,881,2096,4010,27610,27900,27901,27902,54908</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03441715$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Yang, Yi-Cheng</creatorcontrib><creatorcontrib>Kao, Shih-Shun</creatorcontrib><creatorcontrib>Klasing, Ralf</creatorcontrib><creatorcontrib>Hsieh, Sun-Yuan</creatorcontrib><creatorcontrib>Chou, Hsin-Hung</creatorcontrib><creatorcontrib>Chang, Jou-Ming</creatorcontrib><title>The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks</title><title>IEEE access</title><addtitle>Access</addtitle><description><![CDATA[A set of the spanning trees in a graph <inline-formula> <tex-math notation="LaTeX">G </tex-math></inline-formula> is called independent spanning trees if they have a common root <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> and for each vertex <inline-formula> <tex-math notation="LaTeX">v\in V(G)\setminus \{r\} </tex-math></inline-formula>, the paths from <inline-formula> <tex-math notation="LaTeX">v </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> in any two trees are directed edge-disjoint and internally vertex-disjoint. The construction of independent spanning trees has many practical applications in reliable communication networks, such as fault-tolerant transmission and secure message distribution. A burnt pancake network <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> is a kind of Cayley graph, which has been proposed as the topology of an interconnection network. In this paper, we provide a two stages construction scheme that can be used to construct a maximal number of independent spanning trees on a burnt pancake network in <inline-formula> <tex-math notation="LaTeX">O(N\times n) </tex-math></inline-formula> time, where <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> is the number of nodes of <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the dimension of the network. Furthermore, we prove the correctness of our proposed algorithm in constructing independent spanning trees.]]></description><subject>Algorithms</subject><subject>burnt pancake network</subject><subject>Communication networks</subject><subject>Computer Science</subject><subject>Fault tolerance</subject><subject>Fault tolerant systems</subject><subject>fault-tolerant transmission</subject><subject>Graph theory</subject><subject>Independent spanning trees</subject><subject>interconnection networks</subject><subject>Networking and Internet Architecture</subject><subject>Program processors</subject><subject>Roads</subject><subject>secure message distribution</subject><subject>Topology</subject><subject>Trees (mathematics)</subject><subject>Vegetation</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpVUU1P3DAQtSoqFS38Ai6ReuphF48_4vi4RFBWWmirXc6Wk4whS4hTO1vEv8dLECpzmLGe3nua8SPkDOgCgOrzZVlebjYLRhksOBWaafqFHDPI9ZxLnh_99_5GTmPc0VRFgqQ6Jn-2D5iVvo9j2Ndj6_vMu-xm343t0GG26hscMLV-zDaD7fu2v8-2ATFmiXmxDwn_bfvaPmJ2i-OzD4_xhHx1tot4-j5n5O7qcltez9e_fq7K5XpeC8HGuUDU1jVNk_ZooM45q6Sk1gnmHLVQq0qgbYApxqGptATKVZXbgikuVTqTz8hq8m283ZkhtE82vBhvW_MG-HBvbBjbukMDHApqleDaMaEtFloXFvPa5VXFFfDk9WPyerDdJ6vr5docMMqFAAXyHyTu94k7BP93j3E0O58-Ip1qmCg4k1KkMSN8YtXBxxjQfdgCNYfYzBSbOcRm3mNLqrNJ1SLih0JzECkx_grkWpFP</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Yang, Yi-Cheng</creator><creator>Kao, Shih-Shun</creator><creator>Klasing, Ralf</creator><creator>Hsieh, Sun-Yuan</creator><creator>Chou, Hsin-Hung</creator><creator>Chang, Jou-Ming</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>ESBDL</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7SR</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0001-7695-3535</orcidid><orcidid>https://orcid.org/0000-0002-9542-7968</orcidid><orcidid>https://orcid.org/0000-0003-1627-9598</orcidid><orcidid>https://orcid.org/0000-0003-4746-3179</orcidid></search><sort><creationdate>2021</creationdate><title>The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks</title><author>Yang, Yi-Cheng ; Kao, Shih-Shun ; Klasing, Ralf ; Hsieh, Sun-Yuan ; Chou, Hsin-Hung ; Chang, Jou-Ming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c442t-4ee9afddd695d1c632b550af42ff0a1c7b4ead127231db951037b6a8273573043</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>burnt pancake network</topic><topic>Communication networks</topic><topic>Computer Science</topic><topic>Fault tolerance</topic><topic>Fault tolerant systems</topic><topic>fault-tolerant transmission</topic><topic>Graph theory</topic><topic>Independent spanning trees</topic><topic>interconnection networks</topic><topic>Networking and Internet Architecture</topic><topic>Program processors</topic><topic>Roads</topic><topic>secure message distribution</topic><topic>Topology</topic><topic>Trees (mathematics)</topic><topic>Vegetation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, Yi-Cheng</creatorcontrib><creatorcontrib>Kao, Shih-Shun</creatorcontrib><creatorcontrib>Klasing, Ralf</creatorcontrib><creatorcontrib>Hsieh, Sun-Yuan</creatorcontrib><creatorcontrib>Chou, Hsin-Hung</creatorcontrib><creatorcontrib>Chang, Jou-Ming</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE Open Access Journals</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials 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><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>IEEE access</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Yi-Cheng</au><au>Kao, Shih-Shun</au><au>Klasing, Ralf</au><au>Hsieh, Sun-Yuan</au><au>Chou, Hsin-Hung</au><au>Chang, Jou-Ming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks</atitle><jtitle>IEEE access</jtitle><stitle>Access</stitle><date>2021</date><risdate>2021</risdate><volume>9</volume><spage>16679</spage><epage>16691</epage><pages>16679-16691</pages><issn>2169-3536</issn><eissn>2169-3536</eissn><coden>IAECCG</coden><abstract><![CDATA[A set of the spanning trees in a graph <inline-formula> <tex-math notation="LaTeX">G </tex-math></inline-formula> is called independent spanning trees if they have a common root <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> and for each vertex <inline-formula> <tex-math notation="LaTeX">v\in V(G)\setminus \{r\} </tex-math></inline-formula>, the paths from <inline-formula> <tex-math notation="LaTeX">v </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> in any two trees are directed edge-disjoint and internally vertex-disjoint. The construction of independent spanning trees has many practical applications in reliable communication networks, such as fault-tolerant transmission and secure message distribution. A burnt pancake network <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> is a kind of Cayley graph, which has been proposed as the topology of an interconnection network. In this paper, we provide a two stages construction scheme that can be used to construct a maximal number of independent spanning trees on a burnt pancake network in <inline-formula> <tex-math notation="LaTeX">O(N\times n) </tex-math></inline-formula> time, where <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> is the number of nodes of <inline-formula> <tex-math notation="LaTeX">BP_{n} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the dimension of the network. Furthermore, we prove the correctness of our proposed algorithm in constructing independent spanning trees.]]></abstract><cop>Piscataway</cop><pub>IEEE</pub><doi>10.1109/ACCESS.2021.3049290</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0001-7695-3535</orcidid><orcidid>https://orcid.org/0000-0002-9542-7968</orcidid><orcidid>https://orcid.org/0000-0003-1627-9598</orcidid><orcidid>https://orcid.org/0000-0003-4746-3179</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms burnt pancake network Communication networks Computer Science Fault tolerance Fault tolerant systems fault-tolerant transmission Graph theory Independent spanning trees interconnection networks Networking and Internet Architecture Program processors Roads secure message distribution Topology Trees (mathematics) Vegetation |
| title | The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks |
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