On Complementation of Pathsets and Cutsets

Rai, Suresh; Aggarwal, K. K.

doi:10.1109/tr.1980.5220755

Cited by 31 publications

(8 citation statements)

References 3 publications

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“…The construction of the possible paths for a node x from the paths of its predecessors is made by a simple increase of these paths (eq.2). (18,17), (18,19), (12,11), (12,15), (2,4), (2,12), (0,3) (14,17), (17,19), (17,15), (15,20), (17,20), (19,20) 14,17,19,15,20 (16,14), (11,14), (14,17), (17,19), (17,15), (15,20), (17,20), (19,20) 14,17,19,15,20 (4,11), (16,14), (11,14), (14,17), (17,19), (17,15), (1...…”

Section: B the Enumeration Of All Minimal Paths In Directed Graph Wimentioning

confidence: 99%

“…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: B the Enumeration Of All Minimal Paths In Directed Graph Wimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

Housni¹

2019

ijacsa

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“…Network reliability has been a research topic of interest since the early days of reliability engineering, and it has been a popular tool to evaluate and validate the performance of many real-world modern systems [1]- [40] such as grid and cloud computing [9], computer and communication systems [10], sensor networks [11], [12], traffic service networks [13], [14], the Internet of Things [15], [16], system design [17]- [19], and production systems [20].…”

Section: Introductionmentioning

confidence: 99%

“…The definition of (two-terminal) network reliability R is the success probability that there is at least an MP from the source node to the sink node, i.e., the probability for a live connection between a source node and a sink node in a network G(V , E) [1]- [3], where V and E are the node set and edge set: R = Pr({X |source node is connected to sink node in subnetwork G(V , X ) for all X ⊆ E}.…”

Section: Introductionmentioning

confidence: 99%

A New Node-Based Concept for Solving the Minimal Path Problem in General Networks

et al. 2019

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The validation and evaluation of network reliability are significant issues in the planning, design, and control of systems. The minimal path (MP, an edge set) set is one of the main tools used in measuring network reliability. A new node-based concept to find all MPs is proposed by simply searching all of the ordered node subsets with a time complexity O(ne n), where n is the number of nodes. The proposed concept is implemented in a newly proposed node-based MP algorithm using depth-first search (DFS). Because O(m) = O(n 2), where m is the number of edges, the proposed node-based MP algorithm is theoretically more efficient than conventional edge-based algorithms, which all use time complexity O(n2 m) to search for all MPs. Finally, a series of numerical experiments is implemented to test the performance of the proposed algorithm. INDEX TERMS General networks, reliability, minimal path (MP), node-based concept.

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“…Bellmore and Jensen [9] first investigated the search for all minimal cut-sets. Plenty of improved approaches were developed after that, such as Rai and Aggarwal [10] used Boolean algebra to obtain minimal cut-sets by inverting from the minimal cut-sets; Yeh [11] applied a revised layered-network algorithm to search for all minimal paths. Recently some improved approaches are proposed to efficiently determine minimal tie-set and cut-set.…”

Section: Reliability Determination From Tie-set and Cut-setmentioning

confidence: 99%

Development of a software tool for reliability estimation

Li¹

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Development of a Software Tool for Reliability Estimation Chihui Li This thesis presents Version 2.0 of Software Tool for Reliability Estimation (STORE 2.0). It expands on the work done by Parekh [1] by revising the algorithm for tie-set and cut-set calculation, by including fault tree reliability analysis, by analyzing state dependent system, and by integrating component and system reliability analysis. This thesis also presents an approach to the simplification of complex systems by collapsing series and parallel components into a subsystem. The approach was illustrated on an example described by Nelson et al. [2]. The example had 16 components resulting in ten cut-sets and fifty five tie-sets. Upon simplification, the problem was reduced to one tie-set only. STORE 2.0 integrates parameter estimation, component reliability analysis, system reliability analysis, estimation of reliability of state dependent systems, and fault tree analysis. It was verified and validated on several examples taken from the open literature. The software was developed in Visual Basic 2008 with SQL as the database.

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On Complementation of Pathsets and Cutsets

Cited by 31 publications

References 3 publications

An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

A New Node-Based Concept for Solving the Minimal Path Problem in General Networks

Development of a software tool for reliability estimation

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