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An O (| E |) Time Algorithm for Computing the Reliability of a Class of Directed Networks

Author

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  • Avinash Agrawal

    (University of California, Berkeley, California)

  • A. Satyanarayana

    (University of California, Berkeley, California)

Abstract

This paper studies the problem of computing the source-to-terminal reliability, the probability that a source s can communicate with a terminal t , in a probabilistic directed network. It introduces a set of reliability-preserving reductions, called 2-neighbor-node reductions. We show that for a class of directed networks, called BSP-digraphs, such reductions are always admissible and the source-to-terminal reliability can be computed in time linear in the size of the network. A directed network D = ( V , E ) is a BSP-digraph if its underlying undirected graph is series-parallel. The BSP-digraphs considered can be cyclic or acyclic and both vertices as well as edges can fail. Any two vertices can be chosen as s and t . Previously, no polynomial time algorithms were known for this class of digraphs. The proposed method is also applicable to mixed graphs containing directed and undirected edges.

Suggested Citation

  • Avinash Agrawal & A. Satyanarayana, 1984. "An O (| E |) Time Algorithm for Computing the Reliability of a Class of Directed Networks," Operations Research, INFORMS, vol. 32(3), pages 493-515, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:493-515
    DOI: 10.1287/opre.32.3.493
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