New and efficient method to find all minimal paths

Lamalem, Yasser; Housni, Khalid

doi:10.1109/commnet49926.2020.9199616

Cited by 3 publications

(2 citation statements)

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“…The enumeration of all d-minimal pathways (d-MPs) for a certain level d is one of the available approaches [10], [19]- [25] for computing the system dependability of a multi-state system. There are two ways provided in the literature for locating all d-MPs for a certain d. The first one generates d-MPs using direct methods, and the second approach generates d-MPs using pre-enumerated minimal paths (MPs).…”

Section: Introductionmentioning

confidence: 99%

Evaluating multi-state systems reliability with a new improved method

et al. 2022

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The computation of network reliability for a system with many states is an NP-hard issue. Finding all the minimum path vectors (d-MPs) lower boundary points for each level d is one of the few approaches for computing such dependability. This research proposed enhancements to the technique described in Chen's "Searching for d-MPs with rapid enumeration" paper. We propose additional adjustments to the method that creates the flow vector F in this enhancement. This decreases the number of required steps and the temporal complexity of the method. Comparing the newly suggested approach to the old algorithm reveals that the adjustment has increased the enumeration's efficiency and degree of complexity.

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Section: Introductionmentioning

confidence: 99%

Evaluating multi-state systems reliability with a new improved method

et al. 2022

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“…Various methods that serve for the determination of the reliability of a network have been proposed in the literature,and as examples, we can cite [1]- [11]. These methods can be classified into state enumeration methods [1]- [3] and cut/path set enumeration methods [4]- [10].…”

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An Efficient Method to Find All d-MPs in Multistate Two-Terminal Networks

2020

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Many systems in the real-world are multi-state systems composed of multi-state components (nodes and arcs) in which the reliability of the system can be calculated in terms of the lower bound points of level d, called d-Minimal Paths (d-MPs). Such systems (oil/gas production, power transmission and distribution networks, etc.) may be considered as network flows whose arcs have independent and discrete random capacities. In this paper, we present a new algorithm to generate all d-MPs candidates for all d levels. Our algorithm is based on the incremental enumeration of the different d-MPs. In the beginning, we determine the list of all minimal paths (also called 1-MPs). The latter will then be used to generate the 2-MPs. Then from 1-MPS and 2-MPs we generate 3-MPs . . . and so on. The greatest contribution of our method is the use of a technique which makes it possible to know, at each level i, which minimal paths can lead to valid (i+1)-MPs without resorting to an additional validation process. This has reduced the execution time compared to the existing algorithms to find all d-MPs for all possible d values.

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