Resende, M.G.C. (1986) A Program for Reliability Evaluation of Undirected Networks via Polygon-to-Chain Reductions. IEEE Transaction on Reliability, 35, 24-29.
https://doi.org/10.1109/TR.1986.4335334

has been cited by the following article:

• TITLE: System Reliability Evaluation for Imperfect Networks Using Polygon-to-Chain Reduction

  AUTHORS: Mohamed-Larbi Rebaiaia, Daoud Ait-Kadi

  KEYWORDS: Reliability, Networks, Algorithms, Factorization, Polygon-to-Chain Reduction, Decomposition

  JOURNAL NAME: American Journal of Operations Research, Vol.7 No.3, May 22, 2017

  ABSTRACT: The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures. In this computation, a mathematical model is provided using a technique which incorporates the effect of the factoring decomposition theorem using polygon-to-chain and series-parallel reductions. The algorithm proceeds by identifying iteratively one of seven polygons and when it is discovered, the polygon is immediately removed and replaced by a simple chain after having changed the individual values of the reliability of each edge and each node of the polygon. Theoretically, the mathematical development follows the results presented by Satyanarayana & Wood and Theologou & Carlier. The computation process is recursively performed and less constrained in term of execution time and memory space, and generates an exact value of the reliability.