All-Terminal Network Reliability Using Recursive Truncation Algorithm

Sharafat, Ahmad R.; Marouzi, Omid Reza

doi:10.1109/tr.2009.2020120

Cited by 38 publications

(14 citation statements)

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“…Nevertheless, there are algorithms to approximate the all-terminal reliability of a given network. A bounding approximation algorithm, which uses the probability of failure for a union of events in minimal cutsets, can be found in [36]. In fact, to reduce the size of the problem, the authors in [36] use a small portion of the minimal cuts existing in the graph.…”

Section: Background and Related Workmentioning

confidence: 99%

“…A bounding approximation algorithm, which uses the probability of failure for a union of events in minimal cutsets, can be found in [36]. In fact, to reduce the size of the problem, the authors in [36] use a small portion of the minimal cuts existing in the graph. Furthermore, the approximation to the probability of the union of events is calculated recursively and the algorithm can calculate upper and lower bounds on the all-terminal reliability of a given network.…”

Section: Background and Related Workmentioning

confidence: 99%

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An effective algorithm for computing all‐terminal reliability bounds

et al. 2015

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Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

An effective algorithm for computing all‐terminal reliability bounds

et al. 2015

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“…These bounds can be grouped as (1) bounds based on the reliability polynomial (such as Ball andProvan 1983, Van Slyke andFrank 1972) or (2) bounds based on arc packing by cut or path sets (such as Brecht and Colbourn 1988, Lomonosov and Polesskii 1972, Sharafat and Ma'rouzi 2009. The bounds in the first group count operational network states and obtain bounds by counting a fraction of all possible states.…”

Section: A New Upper Boundmentioning

confidence: 99%

Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

Konak¹,

Smith

2011

INFORMS Journal on Computing

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T his paper presents a biobjective genetic algorithm (GA) to design reliable two-node connected telecommunication networks. Because the exact calculation of the reliability of a network is NP-hard, network designers have been reluctant to use network reliability as a design criterion; however, it is clearly an important aspect. Herein, three methods of reliability assessment are developed: an exact reliability calculation method using factoring, an efficient Monte Carlo estimation procedure using the sequential construction technique and network reductions, and an upper bound for the all-terminal reliability of networks with arbitrary arc reliabilities. These three methods of reliability assessment are used collectively in a biobjective GA with specialized mutation operators that perturb solutions without disturbing two-node connectivity. Computational experiments show that the proposed approach is tractable and significantly improves upon the results found by single-objective heuristics.

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“…Thus, it is critical to investigate their trade-offs and superiority over each other. nected (two-terminal reliability [3]), all nodes in the network are pairwise connected (all-terminal reliability [36]), or all nodes in a given subset are pairwise connected (k-terminal reliability [18]).…”

Section: Introductionmentioning

confidence: 99%

An in-depth comparison of s-t reliability algorithms over uncertain graphs

Ke¹,

Khan²,

Quan³

2019

Proc. VLDB Endow.

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Uncertain, or probabilistic, graphs have been increasingly used to represent noisy linked data in many emerging applications, and have recently attracted the attention of the database research community. A fundamental problem on uncertain graphs is the s-t reliability, which measures the probability that a target node t is reachable from a source node s in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence.Due to the inherent complexity of the s-t reliability estimation problem (#P-hard), various sampling and indexing based efficient algorithms were proposed in the literature. However, since they have not been thoroughly compared with each other, it is not clear whether the later algorithm outperforms the earlier ones. More importantly, the comparison framework, datasets, and metrics were often not consistent (e.g., different convergence criteria were employed to find the optimal number of samples) across these works. We address this serious concern by re-implementing six state-ofthe-art s-t reliability estimation methods in a common system and code base, using several medium and large-scale, real-world graph datasets, identical evaluation metrics, and query workloads.Through our systematic and in-depth analysis of experimental results, we report surprising findings, such as many follow-up algorithms can actually be several orders of magnitude inefficient, less accurate, and more memory intensive compared to the ones that were proposed earlier. We conclude by discussing our recommendations on the road ahead. Reliability in uncertain graphsTheory Polynomial-time upper/lower bounds [5,7,8,16,27,35] Representative possible worlds [33,37] Simplified version of reliability problem Most reliable path [9,22,26] Algorithm Sequential Distributed [10, 47] Fundamental s-t reliability query Other queries: top-k query[43], distance-constrained query [20], conditional reliability [23], probabilistic road network query [19], influence maximization [21], etc. Uncertainty reduction: adaptive edge testing [13-15], crowdsourcing [31] Estimator Monte Carlo (MC) sampling [12] Variant of MC: Lazy propagation [30] Recursive estimator: RHH [20], RSS [28] Index scheme BFS Sharing [45] ProbTree [32]Our Focus Figure 2: The broad spectrum of reliability problem over uncertain graphs sive samplings [20,28] and shared possible worlds [45], as well as other indexing methods [32]. With the wide range of algorithms available for estimating the s-t reliability over uncertain graphs, there is an urgent need to realize their trade-offs, and to employ the best algorithm for a given scenario.As depicted in Figure 1, we find serious concerns in the existing experimental comparisons of state-of-the-art reliability estimation algorithms over uncertain graphs. (1) There is no prior work that compared all state-of-the-art methods with each other. It is, therefore, difficult to draw a general conclusion on the superiority and trade-offs of different methods.(2) As shown in Figure 1, with the exceptio...

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All-Terminal Network Reliability Using Recursive Truncation Algorithm

Cited by 38 publications

References 13 publications

An effective algorithm for computing all‐terminal reliability bounds

An effective algorithm for computing all‐terminal reliability bounds

Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

An in-depth comparison of s-t reliability algorithms over uncertain graphs

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