Minimal Cuts up to Third Order in a Planar Graph

This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The algorithm has the advantage of having a linear complexity, which makes the problem tractable as opposed to path oriented methods, where path de...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on reliability Vol. R-33; no. 3; pp. 250 - 256
Main Author: Vilar, Julio
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.1984
Institute of Electrical and Electronics Engineers
Subjects:
Algorithm
Application software
Applied sciences
Computer networks
Distributed computing
Exact sciences and technology
Graph theory
Minimal cut sets
Operational research and scientific management
Operational research. Management science
Planar Graph
Power distribution
Power system modeling
Power systems
Reliability theory
Reliability theory. Replacement problems
Set theory
Tree graphs
Graph theory
Reliability
Algorithm
Planar graph
Network
ISSN:0018-9529, 1558-1721
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The algorithm has the advantage of having a linear complexity, which makes the problem tractable as opposed to path oriented methods, where path determination grows exponentially with the size of the graph. This algorithm can be used when the size of the graph requires computer assistance, and it can simplify the application to large systems, of reliability evaluation techniques based on minimal cuts. The limitation of cuts up to third order has a numerical reason since cuts of higher order often negligibly affect the system indexes. A computer application to a graph that models an urban power distribution network shows the algorithm's capacity to handle complex problems and reduce CPU time.
AbstractList This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The algorithm has the advantage of having a linear complexity, which makes the problem tractable as opposed to path oriented methods, where path determination grows exponentially with the size of the graph. This algorithm can be used when the size of the graph requires computer assistance, and it can simplify the application to large systems, of reliability evaluation techniques based on minimal cuts. The limitation of cuts up to third order has a numerical reason since cuts of higher order often neglibly affect the system indexes.
This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The algorithm has the advantage of having a linear complexity, which makes the problem tractable as opposed to path oriented methods, where path determination grows exponentially with the size of the graph. This algorithm can be used when the size of the graph requires computer assistance, and it can simplify the application to large systems, of reliability evaluation techniques based on minimal cuts. The limitation of cuts up to third order has a numerical reason since cuts of higher order often negligibly affect the system indexes. A computer application to a graph that models an urban power distribution network shows the algorithm's capacity to handle complex problems and reduce CPU time.
Author Vilar, Julio
Author_xml – sequence: 1
  givenname: Julio
  surname: Vilar
  fullname: Vilar, Julio
  organization: Department of Transmission and Distribution; Instituto de Investigaciones Eléctricas; Apartado Postal 475; Cuernavaca, Morelos, MEXICO
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=9012757$$DView record in Pascal Francis
BookMark eNp1kDFPwzAQhS1UJNrCzMDiAbGltR07sUdUQUEqKqrCbDm2oxqlSbCdgX9PorYMSEx3p_ve6d6bgUnTNhaAW4wWGCOxLHYLLDhdMEIwR-wCTDFjPME5wRMwRQjzRDAirsAshM9hpFTwKUBvrnEHVcNVHwPsOxhbWOydN3DrjfXQNVDB91o1ysO1V93-GlxWqg725lTn4OP5qVi9JJvt-nX1uEk0SWlMTF5RSlCVklLwfGg1sXkpTIktz1BqUkZKyrOyQsjokuZZxTIjtNBcYI2NSufg4Xi38-1Xb0OUBxe0rYdXbNsHSSgZnNF8AO9PoApa1ZVXjXZBdn6w5b-lQJjkbMTYEdO-DcHbSmoXVXRtE71ytcRIjjHKYifHGOUpxkG3_KM7X_5fcXdUOGvtL33e_gCdTHxE
CODEN IERQAD
CitedBy_id crossref_primary_10_1109_TR_1987_5222466
Cites_doi 10.1109/TR.1979.5220473
10.1016/0045-7906(81)90009-4
10.1109/T-PAS.1975.31901
ContentType Journal Article
Copyright 1985 INIST-CNRS
Copyright_xml – notice: 1985 INIST-CNRS
DBID AAYXX
CITATION
IQODW
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1109/TR.1984.5221805
DatabaseName CrossRef
Pascal-Francis
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Applied Sciences
EISSN 1558-1721
EndPage 256
ExternalDocumentID 9012757
10_1109_TR_1984_5221805
5221805
Genre orig-research
GroupedDBID -~X
.DC
0R~
29I
4.4
5GY
5VS
6IK
8WZ
97E
A6W
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFO
ACGFS
ACIWK
ACNCT
AENEX
AETIX
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ASUFR
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
EBS
EJD
H~9
IAAWW
IBMZZ
ICLAB
IDIHD
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
OCL
P2P
RIA
RIE
RNS
TN5
VH1
VJK
AAYXX
CITATION
08R
ABPTK
IQODW
RIG
XFK
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c234t-d7f4420f32b987442c2e7b9db1e8603d352b486bf00dcb476f56d9c9c891c1da3
IEDL.DBID RIE
ISSN 0018-9529
IngestDate Sun Nov 09 09:46:18 EST 2025
Sun Oct 29 17:07:37 EDT 2023
Tue Nov 18 22:07:02 EST 2025
Sat Nov 29 01:54:27 EST 2025
Tue Aug 26 16:51:09 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 3
Keywords Graph theory
Reliability
Algorithm
Planar graph
Network
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c234t-d7f4420f32b987442c2e7b9db1e8603d352b486bf00dcb476f56d9c9c891c1da3
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
PQID 24272147
PQPubID 23500
PageCount 7
ParticipantIDs proquest_miscellaneous_24272147
crossref_primary_10_1109_TR_1984_5221805
pascalfrancis_primary_9012757
crossref_citationtrail_10_1109_TR_1984_5221805
ieee_primary_5221805
PublicationCentury 1900
PublicationDate 1984-Aug.
PublicationDateYYYYMMDD 1984-08-01
PublicationDate_xml – month: 08
  year: 1984
  text: 1984-Aug.
PublicationDecade 1980
PublicationPlace New York, NY
PublicationPlace_xml – name: New York, NY
PublicationTitle IEEE transactions on reliability
PublicationTitleAbbrev TR
PublicationYear 1984
Publisher IEEE
Institute of Electrical and Electronics Engineers
Publisher_xml – name: IEEE
– name: Institute of Electrical and Electronics Engineers
References de oliveira (ref5) 1976
ref2
ref1
ref3
berge (ref4) 1973
References_xml – ident: ref2
  doi: 10.1109/TR.1979.5220473
– ident: ref3
  doi: 10.1016/0045-7906(81)90009-4
– year: 1973
  ident: ref4
  publication-title: Graphs and Hypergraphs
– ident: ref1
  doi: 10.1109/T-PAS.1975.31901
– year: 1976
  ident: ref5
  publication-title: Reliability evaluation of electrical systems
SSID ssj0014498
Score 1.2842658
Snippet This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The...
SourceID proquest
pascalfrancis
crossref
ieee
SourceType Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 250
SubjectTerms Algorithm
Application software
Applied sciences
Computer networks
Distributed computing
Exact sciences and technology
Graph theory
Minimal cut sets
Operational research and scientific management
Operational research. Management science
Planar Graph
Power distribution
Power system modeling
Power systems
Reliability theory
Reliability theory. Replacement problems
Set theory
Tree graphs
Title Minimal Cuts up to Third Order in a Planar Graph
URI https://ieeexplore.ieee.org/document/5221805
https://www.proquest.com/docview/24272147
Volume R-33
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 1558-1721
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0014498
  issn: 0018-9529
  databaseCode: RIE
  dateStart: 19630101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT4QwEG7UeNCDb-P67MGDB0EKhdKj2bh60NVs0OyN9EUkUXazC_5-O4DEjXrwRmAKZPqa6cx8H0LnXDBhAhM6voSSnCiWTkyIcTJlNLcbhjB1uODlng2H8XjMn5bQZVcLY4ypk8-MC5d1LF9PVAVHZVfWViAxAJYuMxY1tVpdxIBS3q66dgKHPm9hfIjHr5KRa11r6rbNF3agmlIFEiLF3Ooka8gsfqzL9WYz2Pzfb26hjdaoxNfNKNhGS6bYQevfoAZ3kfeQF_m7FepX5RxXU1xOcPKazzR-BPBNnBdYYGAwEjN8CyDWe-h5cJP075yWLcFRfkBLR7OMUt_LAl9ywLT3lW-Y5FoSE0deoK2lJWkcyczztJKURVkYaa64ijlRRItgH60Uk8IcIMxIqEIpdMCloEqFwnpRgBPGhHWAspD0kPulwVS1UOLAaPGW1i6Fx9NklILK01YVPXTRNZg2KBp_i-6CRjux7vbJQhd1zznEzkPWQ2dfXZbaCQJRD1GYSTVPrQ3CgIzp8PcXH6E1-HyT03eMVspZZU7Qqvoo8_nstB5jn9IFzMM
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT9tAEB4hqAQcoBCqpjTNHjj0gIPXXnu9R4SgqQihigzKzdqXhaXWQYnN7--OY6wi4NCbZY9Xq9nHzOzsfB_AiZBc2tBGXqCwJCdOlJdQar1cWyOcwZC2SRfcT_h0mszn4tcGnHa1MNba5vKZHeFjk8s3C13jUdmZ8xVogoClW8ic1VZrdTkDxkS777olHAWiBfKhvjhLZyMXXLNR28ALG9SQquCVSLlyWsnXdBavdubG3Fzt_19HP8Je61aS8_U8OIANWx7C7j9ggz3wb4qy-OOELupqRepHUi1I-lAsDblF-E1SlEQS5DCSS_IDYayP4O7qMr0Yey1fgqeDkFWe4TljgZ-HgRKIah_owHIljKI2if3QOF9LsSRWue8brRiP8yg2QgudCKqpkeEn2CwXpf0MhNNIR0qaUCjJtI6ki6MQKYxLFwLlEe3D6FmDmW7BxJHT4nfWBBW-yNJZhirPWlX04Xv3w-MaR-N90R5qtBPrXg9eDFH3XWD2POJ9GD4PWeaWCOY9ZGkX9SpzXghHOqYvbzc8hO1xejPJJj-n18ewg11Z3_D7CpvVsrYD-KCfqmK1_NbMt7-o29AM
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%3Ajournal&rft.genre=article&rft.atitle=Minimal+cuts+up+to+third+order+in+a+planar+graph&rft.jtitle=IEEE+transactions+on+reliability&rft.au=Vilar%2C+J&rft.date=1984-08-01&rft.issn=0018-9529&rft.volume=R-33&rft.issue=3&rft.spage=250&rft.epage=256&rft_id=info:doi/10.1109%2FTR.1984.5221805&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9529&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9529&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9529&client=summon