Tolerating a faulty edge in a multi-dimensional mesh
The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a mesh M, find a mesh G which satisfies the following conditions: (1) G and M have the same number of nodes, (2) for any subset of k edges in G,...
Saved in:
Published in | Proceedings of Phoenix Conference on Computers and Communications pp. 9 - 15 |
---|---|
Main Author | |
Format | Conference Proceeding |
Language | English |
Published |
IEEE
1993
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a mesh M, find a mesh G which satisfies the following conditions: (1) G and M have the same number of nodes, (2) for any subset of k edges in G, there is a submesh in G isomorphic to M which excludes these k edges, and (3) G has the least possible number of edges. The mesh G which satisfies these conditions is called a symmetrically optimal k-edge-fault-tolerant (k-EFT) extension of M. It is shown that, even when k=1, finding such a mesh G is a very difficult problem. A necessary and sufficient condition is developed for characterizing the class of symmetrically optimal 1-EFT extensions of any given mesh. Two new methods are proposed based on this characterization for finding symmetrically optimal, or symmetrically near-optimal, 1-EFT extensions. The first method finds an optimal solution, but is useful only for meshes whose number of dimensions is relatively small. The second method finds only a near optimal solution by decomposing a mesh with a large number of dimensions into several meshes with a smaller number of dimensions that can be solved by the first method.< > |
---|---|
AbstractList | The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a mesh M, find a mesh G which satisfies the following conditions: (1) G and M have the same number of nodes, (2) for any subset of k edges in G, there is a submesh in G isomorphic to M which excludes these k edges, and (3) G has the least possible number of edges. The mesh G which satisfies these conditions is called a symmetrically optimal k-edge-fault-tolerant (k-EFT) extension of M. It is shown that, even when k=1, finding such a mesh G is a very difficult problem. A necessary and sufficient condition is developed for characterizing the class of symmetrically optimal 1-EFT extensions of any given mesh. Two new methods are proposed based on this characterization for finding symmetrically optimal, or symmetrically near-optimal, 1-EFT extensions. The first method finds an optimal solution, but is useful only for meshes whose number of dimensions is relatively small. The second method finds only a near optimal solution by decomposing a mesh with a large number of dimensions into several meshes with a smaller number of dimensions that can be solved by the first method.< > |
Author | Farrag, A.A. |
Author_xml | – sequence: 1 givenname: A.A. surname: Farrag fullname: Farrag, A.A. organization: Dept. of Math. & Comput. Sci., Dalhousie Univ., Halifax, NS, Canada |
BookMark | eNotj01LAzEYhANa0NbexVP-wK5vPpscZfELCnrYe0maNzWym5XNeui_N1DnMswchmfW5DpPGQm5Z9AyBvbxs-u6llkrWiGltOyKrGFnQIDlfHdDtqV8Q5VUoK29JbKfBpzdkvKJOhrd77CcKYYT0pRrMdacmpBGzCVN2Q10xPJ1R1bRDQW3_74h_ctz3701-4_X9-5p3yRjl0Z4QKG51iLoisY8BxWdNpWr8rGjgqCNYUZFL53VmodKqIXxhlnlIYoNebjMJkQ8_MxpdPP5cLkl_gBX1UJI |
ContentType | Conference Proceeding |
DBID | 6IE 6IL CBEJK RIE RIL |
DOI | 10.1109/PCCC.1993.344491 |
DatabaseName | IEEE Electronic Library (IEL) Conference Proceedings IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume IEEE Xplore All Conference Proceedings IEEE Xplore IEEE Proceedings Order Plans (POP All) 1998-Present |
DatabaseTitleList | |
Database_xml | – sequence: 1 dbid: RIE name: IEEE Xplore url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Mathematics |
EndPage | 15 |
ExternalDocumentID | 344491 |
GroupedDBID | 6IE 6IK 6IL AAJGR ACGHX ALMA_UNASSIGNED_HOLDINGS BEFXN BFFAM BGNUA BKEBE BPEOZ CBEJK OCL RIB RIC RIE RIL |
ID | FETCH-LOGICAL-i89t-3b0e362663d61101b205fa683441991c50d688185fb4a9662d227638b8195b0f3 |
IEDL.DBID | RIE |
ISBN | 0780309227 9780780309227 |
IngestDate | Wed Jun 26 19:25:13 EDT 2024 |
IsPeerReviewed | false |
IsScholarly | false |
Language | English |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-i89t-3b0e362663d61101b205fa683441991c50d688185fb4a9662d227638b8195b0f3 |
PageCount | 7 |
ParticipantIDs | ieee_primary_344491 |
PublicationCentury | 1900 |
PublicationDate | 19930000 |
PublicationDateYYYYMMDD | 1993-01-01 |
PublicationDate_xml | – year: 1993 text: 19930000 |
PublicationDecade | 1990 |
PublicationTitle | Proceedings of Phoenix Conference on Computers and Communications |
PublicationTitleAbbrev | PCCC |
PublicationYear | 1993 |
Publisher | IEEE |
Publisher_xml | – name: IEEE |
SSID | ssj0000450699 |
Score | 1.2305034 |
Snippet | The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a... |
SourceID | ieee |
SourceType | Publisher |
StartPage | 9 |
SubjectTerms | Concurrent computing Fault tolerance Fault tolerant systems Hypercubes Mathematics Parallel architectures Sufficient conditions |
Title | Tolerating a faulty edge in a multi-dimensional mesh |
URI | https://ieeexplore.ieee.org/document/344491 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjZ3PS8MwFMeD7qQXdU78TQ5e06VJmjTnogxhssOE3UaypDicnbj2oH-9eemsKB68tSmEvobwmvfe9_MQuuFaGqczQUzmFEhyNMmFo0Tx1IQVz1juQY08fpCjR3E_y2ZbznbUwnjvY_GZT-Ay5vLdetFAqGzIhRCgVN_NKWulWl04JfyZUKl1PJjnkDZgTG35Ot39V5aS6uGkKAoQ6vGknfNHb5XoWu4OWs32JhIJoaLkOWlqmyw-fvEa__nWh2jwreHDk847HaEdX_XR_rijtG6OkZiuV8BUDs-xwaVpVvU7hvgaXlZhINYaEgf4_xbdgV_85mmApne302JEtl0UyDLXNeGWekDOSO5kMD21jGalkdBeA6qeFhl1MgevXVphwtmHufClwqa0kGCztOQnqFetK3-KcMmkoqlPtXJcAIdPOauMZxlXwudpeYb6YP38teVkzFvDz_8cvUB7bekgBDMuUa9-a_xVcO-1vY4L-wl6AJ1m |
link.rule.ids | 310,311,786,790,795,796,802,4069,4070,27958,55109 |
linkProvider | IEEE |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PT4MwFG7MPKgXdc74Ww5eYYWWlp6Jy9Rt2QGT3ZZ2LXFxgnFw0L_evjIxGg_eoCQNj6b56Hvf9z2EbohgUouY-jLWHCQ5wk-oxj4nobQrHkeJATXyeMKGj_R-Fs82PttOC2OMceQzE8Clq-XrclFDqqxPKKWgVN-2MI9FI9ZqEyr23wQzIdzRPIHCQRTxjcNOe_9Vp8SiP03TFKR6JGhm_dFdxYHLYL9Rba-dJyFwSp6DulLB4uOXY-M_3_sA9b5VfN60xadDtGWKLtobtz6t6yNEs3IFrsr2uSe9XNar6t2DDJu3LOyAYxv6GhoANOYd3otZP_VQNrjN0qG_6aPgLxNR-URhA6YzjGhmQw9VhONcMmiwAbynRYw1SwC3c0WlPf1E2n4puy0VlNgUzskx6hRlYU6Ql0eM49CEgmtCwYmPa8WliWLCqUnC_BR1Ifr5a-OUMW8CP_tz9BrtDLPxaD66mzyco92GSAipjQvUqd5qc2nBvlJXbpE_AQLWoLw |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=Proceedings+of+Phoenix+Conference+on+Computers+and+Communications&rft.atitle=Tolerating+a+faulty+edge+in+a+multi-dimensional+mesh&rft.au=Farrag%2C+A.A.&rft.date=1993-01-01&rft.pub=IEEE&rft.isbn=9780780309227&rft.spage=9&rft.epage=15&rft_id=info:doi/10.1109%2FPCCC.1993.344491&rft.externalDocID=344491 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9780780309227/lc.gif&client=summon&freeimage=true |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9780780309227/mc.gif&client=summon&freeimage=true |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9780780309227/sc.gif&client=summon&freeimage=true |