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Sixty Years of Network Reliability

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Abstract

The study of network reliability started in 1956 with a groundbreaking paper by E.F. Moore and C.E. Shannon. They introduced a probabilistic model of network reliability, where the nodes of the network were considered to be perfectly reliable, and the links or edges could fail independently with a certain probability. The problem is to determine the probability that the network remains connected under these conditions. If all the edges have the same probability of failing, this leads to the so-called reliability polynomial of the network. Sixty years later, a lot of research has accumulated on this topic, and many variants of the original problem have been investigated. We review the basic concepts and results, as well as some recent developments in this area, and we outline some important research directions.

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Acknowledgements

This paper has grown out of the lectures given at the CIMPA Research School on Mathematical Models for Security Applications, held in Havana, Cuba, from Aug. 29 to Sep. 9, 2016. The author wishes to thank the organizers of the school: Christian Maduit, from CIMPA, Josep M. Miret, from the University of Lleida, Luis R. Piñeiro and Valentina Badia at the University of Havana, as well as the Dept. of Mathematics, University of Lleida, for the support given to the school, in general, and to this author in particular. The author has also been partially supported by Project MTM2013-46949-P, from the Spanish Ministry of Economy and Competitiveness. Professors Charles Colbourn, Dirk Vertigan and Ilya Gertsbakh have provided some useful pointers to the literature, and have kindly answered some questions related to their work. Special thanks are given to the guest editors for their work, and to the reviewers, who made suggestions that have led to the improvement of the manuscript.

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  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, C.P. 43007, Tarragona, Spain

    Hebert Pérez-Rosés

  2. University of Newcastle, Newcastle, Australia

    Hebert Pérez-Rosés

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In loving memory of Prof. Mirka Miller (1949–2016).

This paper has grown out of the lectures given at the CIMPA Research School on Mathematical Models for Security Applications, held in Havana, Cuba, from Aug. 29 to Sep. 9, 2016.

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Pérez-Rosés, H. Sixty Years of Network Reliability. Math.Comput.Sci. 12, 275–293 (2018). https://doi.org/10.1007/s11786-018-0345-5

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