Enumeration of node cutsets for an s-t network

Singh, Brijendra Pratap

doi:10.1016/0026-2714(94)90095-7

Cited by 11 publications

(9 citation statements)

References 5 publications

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“…This section will present the Singh B. [13] algorithm that finds all the minimal nodes cutsets in a graph, and all the steps of the algorithm. The algorithm at the first step accept as inputs the incidence matrix of the graph (I), and a set of nodes (Pm) that contain all the nodes in the shortest minimal path, except two, the source and terminal nodes.…”

Section: Sing B Algorithmmentioning

confidence: 99%

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An Improved Algorithm for Network Reliability based on Finding all Node Cutsets

Lamalem¹

2020

IJATCSE

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We can define the network reliability as the ability of a network to carry out a desired operation such as communication. In the literature, several methods have been proposed to evaluate the reliability of networks. We can cite as an example state enumeration methods and cut/path set enumeration methods. The algorithm proposed by BRIJENDRA SINGH in his paper titled "ENUMERATION OF NODE CUTSETS FOR AN s-t NETWORK" belongs to the category of methods which are based on the enumeration of the minimal node cuts set. This paper is made for the purpose to improve the Singh's algorithm. The improvement includes the efficiency of the algorithm and the execution time.

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Section: Sing B Algorithmmentioning

confidence: 99%

“…Few of the methods consider that the nodes are unreliable and the edges are perfectly reliable as Singh B. [13] , Prasad VC, Sankar V, Prasaka Rao KS [11] and Prasad VC [12].…”

Section: Introductionmentioning

confidence: 99%

An Improved Algorithm for Network Reliability based on Finding all Node Cutsets

Lamalem¹

2020

IJATCSE

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“…In any of the above cases, the main objective is to define the minimum efficiency or inefficiency paths (minimal cut set) between the source (s-source) and each consumer (t-sink node). A number of algorithms based on graph theory [5,14,17,18] have been developed to solve this problem. Zhibin [19] suggested the development of these methods.…”

Section: Introductionmentioning

confidence: 99%

Impact Assessment of Distribution Network Layout on the Reliability of Water Delivery

Kowalski

Kowalska

Bławucki

et al. 2019

Water

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The process of shaping distribution network structures is one of the most fundamental design tasks, and determines the delivery certainty of media transported by them. It is especially crucial with reference to network elements of a critical character, such as roads or water supply, sewage, or electrical networks. In urban conditions, the geometric shaping of these structures has a quasi-chaotic character that is individual for each network and city. The complexity of these networks increases significantly with the size of a city, and therefore the evaluation of water delivery certainty is also a difficult issue. Despite many years of research, there is no universal method to evaluate this certainty. The objective of this paper is to present two original approaches: the number of minimal efficiency paths from a water source to reference consumption nodes, and the relation of this number to the fractal dimension of a network’s geometric structure. The developed methods were tested in the conditions of a few real water supply networks. The obtained results indicate that the analyzed methods can be used for the preliminary and relatively rapid evaluation of water delivery certainty.

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“…Considering properties of each of the aforementioned cases, the estimation methods of water delivery certainty are mainly focused on defining minimal cut sets in s-t networks (ssource, t -sink node). There is a range of algorithms to define minimal cut sets, and they are mainly based on graph theory [12]- [15]. An interesting suggestion of such an algorithm was put forward by Zhibin [16].…”

Section: Introductionmentioning

confidence: 99%

Proposition of Fractal Dimension Application for the Estimation of Certainty of Water Delivery

Kowalski

Kowalska

Suchorab

et al. 2018

WIT Transactions on the Built Environment

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One of the most difficult steps during evaluating of the system safety plan is the evaluation of certainty of water delivery through the distribution network. So far, no universal method of this estimation has been fully elaborated. Most often, the various reliability factors are used. However, these factors does not always include the geometrical structure of distribution network. It can be analysed by methods of minimal cut or efficiency sets paths between water source and outtake or even all nodes. However, such methods are very laborious and their difficulty increases together with the increase of degree of network complexity. The aim of this paper is to present a proposition of an application of two methods: reference nodes and fractal dimension, for estimation of certainty of water delivery though complex distribution networks. Exemplary calculation presented in the paper, were conducted for 6 different models and real water supply networks. The conducted calculations indicated that reference nodes method has a limitation to maximum 6 looped networks. Fractal dimension method doesn't have such limitation. The proved in the paper relationship between fractal dimension value and number of minimal efficiency sets paths indicates that this method can be used for complex networks estimation.

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Enumeration of node cutsets for an s-t network

Cited by 11 publications

References 5 publications

An Improved Algorithm for Network Reliability based on Finding all Node Cutsets

An Improved Algorithm for Network Reliability based on Finding all Node Cutsets

Impact Assessment of Distribution Network Layout on the Reliability of Water Delivery

Proposition of Fractal Dimension Application for the Estimation of Certainty of Water Delivery

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