A Comparison of Four Monte Carlo Methods for Estimating the Probability of s-t Connectedness

Fishman, George S.

doi:10.1109/tr.1986.4335388

Cited by 122 publications

(91 citation statements)

References 16 publications

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“…All estimators studied in this paper will be proven to be the unbiased estimators of R d s,t (G). Thus, the key criterion to discriminate them is their variance [18,6].…”

Section: Computational Complexity and Estimation Criteriamentioning

confidence: 99%

Distance-constraint reachability computation in uncertain graphs

et al. 2011

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Driven by the emerging network applications, querying and mining uncertain graphs has become increasingly important. In this paper, we investigate a fundamental problem concerning uncertain graphs, which we call the distance-constraint reachability (DCR) problem: Given two vertices s and t, what is the probability that the distance from s to t is less than or equal to a user-defined threshold d in the uncertain graph? Since this problem is #P-Complete, we focus on efficiently and accurately approximating DCR online. Our main results include two new estimators for the probabilistic reachability. One is a Horvitz-Thomson type estimator based on the unequal probabilistic sampling scheme, and the other is a novel recursive sampling estimator, which effectively combines a deterministic recursive computational procedure with a sampling process to boost the estimation accuracy. Both estimators can produce much smaller variance than the direct sampling estimator, which considers each trial to be either 1 or 0. We also present methods to make these estimators more computationally efficient. The comprehensive experiment evaluation on both real and synthetic datasets demonstrates the efficiency and accuracy of our new estimators.

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“…All estimators studied in this paper will be proven to be the unbiased estimators of R d s,t (G). Thus, the key criterion to discriminate them is their variance [18,6].…”

Section: Computational Complexity and Estimation Criteriamentioning

confidence: 99%

Distance-constraint reachability computation in uncertain graphs

et al. 2011

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“…Monte Carlo simulation was also used for estimating the single-layer reliability for some fixed link failure probability [11]- [13]. Using simulation, the reliability can be approximated to an arbitrary accuracy, but the number of required iterations tends to be very large especially when the failure probability is small.…”

Section: Previous Workmentioning

confidence: 99%

Reliability in Layered Networks with Random Link Failures

Lee

Modiano

2010

2010 Proceedings IEEE INFOCOM

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Abstract-We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multi-layer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

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“…There are two main approaches the exact calculation through analytic methods (Ball & Van-Slyke 1977, Jan 1993) and the estimation calculation through Monte Carlo simulation (Fishman 1986, Ramirez-Marquez & Coit 2005. For the all-terminal network reliability problem, efficient simulation is difficult because these methods generally lose efficiency as a network approaches a fully connected state.…”

Section: Reliability Calculationmentioning

confidence: 99%