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Computing the SKT reliability of acyclic directed networks using factoring method

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Abstract

This paper presents a factoring algorithm for computing source-to-K terminal (SKT) reliability, the probability that a sources can send message to a specified set of terminalsK, in acyclic directed networks (AD-networks) in which both nodes and edges can fail. Based on Pivotal decomposition theorem, a new formula is derived for computing the SKT reliability of AD-networks. By establishing a topological property of AD-networks, it is shown that the SKT reliability of AD-networks can be computed by recursively applying this formula. Two new Reliability-Preserving Reductions are also introduced. The recursion tree generated by the presented algorithm has at most 2(⋎V⋎-⋎K⋎-⋎C⋎) leaf nodes, where ⋎V⋎ and ⋎K⋎ are the numbers of nodes and terminals, respectively, while ⋎C⋎ is the number of the nodes satisfying some specified conditions. The computation complexity of the new algorithm isO(⋎E⋎·⋎V⋎·2(⋎V⋎-⋎K⋎-⋎C⋎)) in the worst case, where ⋎E⋎ is the number of edges. For source-to-all-terminal (SAT) reliability, its computation complexity isO(⋎E⋎). Comparison of the new algorithm with the existing ones indicates that the new algorithm is more efficient for computing the SKT reliability of AD-networks.

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Authors and Affiliations

  1. Department of Computer Science, Northeastern University, 110006, Shenyang, P. R. China

    Kong Fanjia & Wang Guangxing

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  1. Kong Fanjia
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  2. Wang Guangxing
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Correspondence to Kong Fanjia.

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KONG Fanjia is an Associate Professor of applied mathematics at the Northeastern University, China. He received his B.S. and M.S. degrees in applied mathematics in 1987 and 1990, respectively, and received his Ph.D. degree in computer application in 1998, all from Northeastern University. His research interests are network reliability and fault tolerant computing.

WANG Guangxing was born in 1937. He graduated from the Automatic Control Department, Northeastern University in 1962. From 1980 to 1982, he was a visiting scholar at Rensselaer Polytechnic Institute, Troy, NY. Now he is a Professor at Northeastern University. His research interests include network reliability, fault tolerant computing, and broadband local area networks. He is the author of over 100 publications.

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Kong, F., Wang, G. Computing the SKT reliability of acyclic directed networks using factoring method. J. Comput. Sci. & Technol. 14, 56–63 (1999). https://doi.org/10.1007/BF02952488

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  • DOI: https://doi.org/10.1007/BF02952488

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