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An effective algorithm for computing all-terminal reliability bounds

Jaime Silva, Teresa Gomes, David Tipper, Lúcia Martins, Velin Kounev

2015
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Networks
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The exact calculation of all-terminal reliability is not feasible in large networks. Hence estimation techniques and lower and upper bounds for all-terminal reliability have been utilized. Here, we propose using an ordered subset of the mincuts and an ordered subset of the minpaths to calculate an all-terminal reliability upper and lower bound, respectively. The advantage of the proposed new approach results from the fact that it does not require the enumeration of all mincuts or all minpaths
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... re-1 "This is the peer reviewed version of the following article: Silva, J., Gomes, T., Tipper, D., Martins, L., and Kounev, V. (2015), An effective algorithm for computing all-terminal reliability bounds. NETWORKS, 66: 282-295. doi:10.1002/net.21634, which has been published in final form at https://doi.org/10.1002/net.21634. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving." quired by other bounds. The proposed algorithm uses maximally disjoint minpaths, prior to their sequential generation, and also uses a binary decision diagram for the calculation of their union probability. The numerical results show that the proposed approach is computationally feasible, reasonably accurate and much faster than the previous version of the algorithm. This allows one to obtain tight bounds when it not possible to enumerate all mincuts or all minpaths as revealed by extensive tests on real-world networks. Nowadays communication networks are ubiquitous in our daily life, being one of the critical infrastructures that our society depends on. This leads to concerns about the reliability and resilience of communication when subjected to failures and attacks [42]. A communication network failure is defined as an event where it is not possible to deliver communication services [42]. A network failure can typically occur due to cable cuts, natural disasters and physical/electronic attacks. Due to the importance of communication networks in today's society there is an interest in knowing the network resilience to a potential failure. According to [1], reliability is the "probability that an item will perform a required function under stated conditions for a given time interval". Thence the ability of a network to execute a desired network operation is related to network reliability [11] . In [41] a systematic architectural framework that unifies resilience disciplines, strategies, principles and analysis is presented. The ResiliNets strategy, according to the authors, leads to a set of design principles which can steer the analysis and design of resilient networks. In communication networks, edges may fail, and are either in an operational or failed state. The problem of finding the probability that k specific vertices remain connected is termed, for k=2, the two-terminal reliability problem; when k is equal to the number of vertices in the network, the problem is designated as the all-terminal reliability problem. In the two-terminal reliability problem the main objective is the calculation of the probability of communication between two vertices, i.e., two vertices communicate if there exists at least one operational path that connects the two vertices. For the all-terminal reliability

doi:10.1002/net.21634
fatcat:5z7e5myr5remjh3iof6fn3geie