An Improved Method to Search All Minimal Paths in Networks

Minimal paths (MPs) play an important role in system reliability analysis, such as binary network reliability evaluation and multistate network reliability evaluation. Searching all MPs is an NP-hard problem. The direct-search-based algorithm implements the depth-first search (DFS) mechanism to find...

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Vydáno v:IEEE transactions on reliability Ročník 72; číslo 4; s. 1420 - 1431
Hlavní autoři: Zhou, Xinxin, Bai, Guanghan, Tao, Junyong, Xu, Bei
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Backtracking
Cut set
minimal paths (MPs)
Network reliability
node position
Nodes
NP-hard problem
parallel algorithm
Power transmission
recursive algorithm
Reliability
Reliability analysis
Searching
Stochastic processes
Symbols
System reliability
Transportation
Transportation networks
ISSN:0018-9529, 1558-1721
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Shrnutí:Minimal paths (MPs) play an important role in system reliability analysis, such as binary network reliability evaluation and multistate network reliability evaluation. Searching all MPs is an NP-hard problem. The direct-search-based algorithm implements the depth-first search (DFS) mechanism to find all MPs, which is a simple and efficient method. The current efficient DFS algorithm is based on backtracking and linked list by nodes. In this article, we propose several improvements to speed up the current algorithm. First, we find that the relative positional information of the network can be used to avoid visiting some unnecessary nodes. Thus, we improve the algorithm by incorporating the point in the polygon algorithm to avoid visiting nodes surrounded by other nodes in a network. Second, we further improve the current backtracking condition in which the time complexity of implementing each backtrack is reduced. In addition, we find that different search branches from a similar node are independent and can be executed in parallel. A parallel search mechanism is proposed and incorporated to speed up the searching process. Through computational experiments on several benchmark networks and real transportation networks, we demonstrate that the improved algorithm is more efficient than the existing algorithm. The proposed algorithm becomes more advantageous as the size of the network grows.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2023.3234055