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...

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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
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.1984.5221805