A new technique in a cutset evaluation

Elias, Simone; Mokhles, N.A.; Ibrahim, S.A.

doi:10.1016/0026-2714(93)90135-l

Cited by 12 publications

(2 citation statements)

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“…The evaluation of the reliability of a system that can be modeled as a network can be made in terms of either minimal cuts (MCs) or minimal paths (MPs) [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. In [11], [10], [12], [13], [14] it was shown that the set of all minimal paths can be used for generating all the minimal cut-sets of a graph and vice-versa.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

Housni¹

2019

ijacsa

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The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to generate all minimal paths in a graph G(V, E). The algorithm proposed builds the set of minimal paths gradually, starting from the source node s. We present two versions of our algorithm; the first version determines all feasible paths between a pair of terminals in a directed graph without cycle, and this version runs in linear time O(|V | + |E|). The second version determines all minimal paths in a general graph (directed and undirected graph). In order to show the process and the effectiveness of our method, an illustrative example is presented for each case.

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Section: Introductionmentioning

confidence: 99%

“…7,6,8,9),(3,1,4,5,6,8,9),(3,7,8,9)}; P3,10={(3,1,4,5,10),(3,7,6,8,9,10),(3,1,4,5,6,8,9,10), (3,7,8,9,10) }13{13}13 P3,9, P3,10 P3,3={}; P3,1={}; P3,4={}; P3,5={}; P3,7={}; P3,6={}; P3,8={}; P3,9={}; P3,10={}; P3,13={(3,1,4,5,10,13),(3,7,6,8,9,10,13),(3,1,4,5,6,8,9,10,13),(3,7,8,…”

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confidence: 99%