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Computing Network Reliability in Time Polynomial in the Number of Cuts

Author

Listed:
  • J. Scott Provan

    (National Bureau of Standards, Washington, D. C. and University of North Carolina, Chapel Hill, North Carolina)

  • Michael O. Ball

    (University of Maryland, College Park, Maryland)

Abstract

We present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network. The computation time of this algorithm is bounded by a polynomial in the number of ( s , t )-cuts in the network. We also examine the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network. These problems are distinguished as either having algorithms that are polynomial in the number of such sets, or having no such algorithms unless P = NP .

Suggested Citation

  • J. Scott Provan & Michael O. Ball, 1984. "Computing Network Reliability in Time Polynomial in the Number of Cuts," Operations Research, INFORMS, vol. 32(3), pages 516-526, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:516-526
    DOI: 10.1287/opre.32.3.516
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    Cited by:

    1. Grit Claßen & Arie M. C. A. Koster & David Coudert & Napoleão Nepomuceno, 2014. "Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 893-909, November.
    2. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2016. "Connectivity reliability and topological controllability of infrastructure networks: A comparative assessment," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 24-33.
    3. Sharma, Megha & Ghosh, Diptesh, 2009. "Computing the probability mass function of the maximum flow through a reliable network," IIMA Working Papers WP2009-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. Goharshady, Amir Kafshdar & Mohammadi, Fatemeh, 2020. "An efficient algorithm for computing network reliability in small treewidth," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    5. Jane, Chin-Chia & Yuan, John, 2001. "A sum of disjoint products algorithm for reliability evaluation of flow networks," European Journal of Operational Research, Elsevier, vol. 131(3), pages 664-675, June.

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