A new efficient algorithm for finding all d -minimal cuts in multi-state networks

Niu, Yifeng; Gao, Ziyou; Lam, William H. K.

doi:10.1016/j.ress.2017.05.032

Cited by 38 publications

(15 citation statements)

References 56 publications

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“…Recently, Yeh proposed the first node-based MP algorithm to search for all MPs in a directed acyclic network by finding the longest path in each selected node subset [43]. The time complexity in Yeh's algorithm is O(m2n m ), which is the first instance of the time complexity of the MP algorithm being equal to that of the best-known minimal cut (MC) algorithm (also node-based) in the literature [48], [49]. However, the directed acyclic network is only applicable for some special networks without any cycles, and it is also an NP-hard problem to find the longest path [43], i.e., Yeh's method is not applicable for general networks where cycles are always included.…”

Section: There Are Different Methods Used For Calculating Networkmentioning

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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Section: There Are Different Methods Used For Calculating Networkmentioning

confidence: 99%

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

et al. 2019

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“…Use the comparison method to check whether x i 1 ≤ i ≤ λ is a d-minimal path or not. Furthermore, it is calculated that the proposed algorithm needs to perform 21 enumerations during the solution of 3minimal path candidates, i.e., solving conditions (10)- (19). By contrast, if the method by Chen and Lin [22] is used to solve 3-minimal path candidates of the network, it needs to perform a total of 28 enumerations.…”

Section: Inputmentioning

confidence: 99%

“…Reliability evaluation is a powerful tool for the demonstration of network performance. For a stochastic-flow network, the reliability index R d is defined as the probability that at least d units of flow (i.e., commodity demand) can be successfully transmitted from the source to the destination through stochastic arc capacities [14][15][16][17][18][19][20][21][22]. To date, many studies [14-18, 21, 22] have evaluated the reliability R d in terms of d-minimal paths.…”

Section: Introductionmentioning

confidence: 99%

Performance Assessment of a Freight Network with Stochastic Capacities

Niu

2018

Complexity

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This paper focuses on performance assessment of a freight network with stochastic capacities by using reliability analysis, in which a node denotes a supplier, a transfer center, a distribution center, or a market, while an arc denotes a logistics service provider offering the freight traffic service for a pair of nodes. Due to some uncertainties in real environment (for example, a proportion of vehicles owned by the provider may be reserved by other customers), the available capacity of the provider along each arc is stochastic. Thus, network reliability that at least d units of commodity demand can be successfully delivered from the source to the destination denotes the operational performance of such a freight network. A d-minimal path–based method is developed to evaluate the freight network reliability. To advance the efficiency of solving d-minimal paths, an improved model is established by redefining capacity bounds of arcs and minimal paths. Furthermore, a new concept of expected capacity grounded on network reliability is presented to measure the service performance of the freight network. A practical case related to the coal delivery network is studied to demonstrate the implications of both network reliability and expected capacity.

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“…A prominent related problem is the two-terminal multistate reliability evaluation, which is now considered as a classical network reliability problem. Several methods have been developed that focus on this problem as well as provide critical insights into multistate modelling in general [6][7][8][9][10][11][12][13][14][15]. This paper examines two methods of evaluating the reliability of multistate flow networks.…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

Rushdi

Alsalami

2020

JERR

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This paper examines two simple (albeit useful) methods used to evaluate the reliability of two-terminal multistate flow networks. These two methods involve two Karnaugh map versions, namely the Variable-Entered Karnaugh Map (VEKM) and the Multi-Valued Karnaugh Map (MVKM). These two versions are crucial in providing not only the visual insight necessary to write better future software but also adequate means of verifying such software. We assess these two versions of map methods versus the exhaustive search method, which guarantees conceptual clarity at the expense of lack of computational efficiency. Our target is the evaluation of the probability mass function (pmf) in a wide array of cases, in which we consider flow from a source node to a sink node in a capacitated network with a multistate capacity model for the links. Each network link has a varying capacity, which is assumed to exist in a mutually exclusive sense. The reliability of the system is wholly dependent on its ability to successfully transmit at least a certain required system flow from the source (transmitter) to the sink (receiver) station. The max-flow min-cut theorem is critical in obtaining all successful states. To demonstrate the proposed methods applicability, two demonstrative examples are given with ample details.

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A new efficient algorithm for finding all d -minimal cuts in multi-state networks

Cited by 38 publications

References 56 publications

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

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

Performance Assessment of a Freight Network with Stochastic Capacities

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

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