An effective algorithm for computing all‐terminal reliability bounds

Silva, Jaime; Gomes, Teresa; Tipper, David; Martins, Lucia; Kounev, Velin

doi:10.1002/net.21634

Cited by 23 publications

(17 citation statements)

References 45 publications

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“…In [11] and [12] an algorithm is proposed for calculating lower and upper bounds for the all terminal reliability 1 . This algorithm uses an ordered subset of the cutsets to calculate the reliability upper bound and an ordered subset of the pathsets (spanning trees) to calculate the reliability lower bound.…”

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

“…This means that, unlike in the exact method, it is not necessary to enumerate all cutsets or pathsets, which quickly becomes prohibitively slow. A more thorough description of this approach can be found in [11], [12].…”

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

“…The algorithm keeps generating increasingly tight upper and lower bounds until the desired difference between the two is obtained, a time limit is reached or some topologically based conditions are verified (see [11], [12] for more details). In [11] the calculation of the probability of disjoint events was done using algorithm KDH88 [20].…”

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

“…Every sequentially selected cutset and pathset is considered in this algorithm. A more effective algorithm is presented in [12] where, similarly to the approach in [21], the pathsets and cutsets that do not contribute significantly to reducing the reliability gap are ignored. Also in [12] the maximally disjoint pathsets are first considered, followed by the pathsets generated by decreasing probability.…”

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

“…In the next section we will talk about reductions of the network, which will be used by both approaches. In Section III we explain the method used in [11] and [12] that uses iterative path-and cutset enumeration. In Section IV the decomposition method proposed in [13] and [14] will be explained.…”

mentioning

confidence: 99%

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A Comparison between Two All-Terminal Reliability Algorithms

Pino¹,

Gomes²,

Kooij³

2015

JACN

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Abstract-Two algorithms computing the all-terminal reliability are compared. The first algorithm uses the pathsets and cutsets of the network to find lower and upper bounds respectively. The second algorithm uses decomposition and is able to give an exact outcome. The latter approach is significantly faster and able to calculate the exact value. However, for some large networks the decomposition algorithm does not give results while the path-and cutset algorithm still returns bounds. The low computation times of the proposed decomposition algorithm make it feasible to incorporate the repeated calculation of the all-terminal reliability in new types of network analysis. Some illustrations of these analyses are provided. IndexTerms-All-terminal network reliability, decomposition, network availability, pathwidth.

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Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

Section: Iterative Pathset and Cutset Generationmentioning

confidence: 99%

mentioning

confidence: 99%

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A Comparison between Two All-Terminal Reliability Algorithms

Pino¹,

Gomes²,

Kooij³

2015

JACN

Self Cite

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An optimization‐based Monte Carlo method for estimating the two‐terminal survival signature of networks with two component classes

Lopes da Silva,

Sullivan

2024

Naval Research Logistics

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Evaluating two‐terminal network reliability is a classical problem with numerous applications. Because this problem is ‐Complete, practical studies involving large systems commonly resort to approximating or estimating system reliability rather than evaluating it exactly. Researchers have characterized signatures, such as the destruction spectrum and survival signature, which summarize the system's structure and give rise to procedures for evaluating or approximating network reliability. These procedures are advantageous if the signature can be computed efficiently; however, computing the signature is challenging for complex systems. With this motivation, we consider the use of Monte Carlo (MC) simulation to estimate the survival signature of a two‐terminal network in which there are two classes of i.i.d. components. In this setting, we prove that each MC replication to estimate the signature of a multi‐class system entails solving a multi‐objective maximum capacity path problem. For the case of two classes of components, we adapt a Dijkstra's‐like bi‐objective shortest path algorithm from the literature for the purpose of solving the resulting bi‐objective maximum capacity path problem. We perform computational experiments to compare our method's efficiency against intuitive benchmark approaches. Our computational results demonstrate that the bi‐objective optimization approach consistently outperforms the benchmark approaches, thereby enabling a larger number of MC replications and improved accuracy of the reliability estimation. Furthermore, the efficiency gains versus benchmark approaches appear to become more significant as the network increases in size.

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Network reliability: Heading out on the highway

et al. 2020

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A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

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An effective algorithm for computing all‐terminal reliability bounds

Cited by 23 publications

References 45 publications

A Comparison between Two All-Terminal Reliability Algorithms

A Comparison between Two All-Terminal Reliability Algorithms

An optimization‐based Monte Carlo method for estimating the two‐terminal survival signature of networks with two component classes

Network reliability: Heading out on the highway

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