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Combinatorial aspects of network reliability

  • Section I General Topological Network Design
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Abstract

This is a short tutorial introduction to combinatorial aspects of network reliability, focusing on recent results in the area. Topics include the complexity of reliability computations, exact algorithms, bounding methods and Monte Carlo strategies.

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References

  1. H.M.F. Abo El Fotoh, Reliability of radio broadcast networks: A graph-theoretic approach, Ph.D. Thesis, University of Waterloo (1988).

  2. H.M.F. Abo El Fotoh and C.J. Colbourn, Series-parallel bounds for the two-terminal reliability problem, ORSA J. Comp. 1(1989)209–222.

    Google Scholar 

  3. T.B. Boffey, C.J. Colbourn and L.D. Nel, Probabilistic estimation of damage from fire spread, in preparation.

  4. M. Chari, Combinatorial aspects of degeneracy in linear systems and network reliability, Ph.D. Thesis, Operations Research, University of North Carolina at Chapel Hill (1990).

  5. M. Chari and J.S. Provan, On the use of shellings and partitions in computing two-terminal reliability,CORS/TIMS/ORSA Meeting, Vancouver (1989).

  6. C.J. Colbourn,The Combinatorics of Network Reliability (Oxford University Press, Oxford and New York, 1987).

    Google Scholar 

  7. C.J. Colbourn, A note on boundingk-terminal reliability, Algorithmica, to appear.

  8. C.J. Colbourn, R.P.J. Day and W.J. Myrvold, Generating random spanning trees efficiently, Preprint (1989).

  9. C.J. Colbourn, R.P.J. Day and L.D. Nel, Unranking and ranking spanning trees of a graph, J. Algorithms 10(1989)271–286.

    Google Scholar 

  10. C.J. Colbourn and W.R. Pulleyblank, Matroid Steiner problems, the Tutte polynomial and network reliability, J. Combin. Theory B47(1989)20–31.

    Google Scholar 

  11. T.A. Feo and J.S. Provan, Delta-wye transformations and the efficient reduction of two-terminal planar graphs, Oper. Res., to appear.

  12. G.S. Fishman, A Monte Carlo plan for estimating reliability parameters and related functions, Networks 17(1987)169–186.

    Google Scholar 

  13. A. Kanevsky, Graphs with odd and even edge connectivities are inherently different, Report TAMU-89-010, Texas A&M University (1989).

  14. V.A. Kaustov, Ye.I. Litvak and I.A. Ushakov, The computational effectiveness of reliability estimates by the method of nonedge-intersecting chains and cuts, Sov. J. Comp. Syst. Sci. 24 (4) (1986)59–62.

    Google Scholar 

  15. A.B. Lehman, Wye-delta transformations in probabilistic networks, J. SIAM 11(1963)773–805.

    Google Scholar 

  16. Ye.I. Litvak, A generalized delta-star transformation in the investigation of properties of complex networks, Eng. Cybern. 19(1981).

  17. Ye.I. Litvak and I.A. Ushakov, Estimation of the parameters of structurally complex systems, Eng. Cybern. 22 (3) (1984)35–49.

    Google Scholar 

  18. C.I. Liu and Y. Chow, Enumeration of connected spanning subgraphs of a planar graph, Acta Math. Hung. 41(1983)27–36.

    Google Scholar 

  19. M.V. Lomonosov and V.P. Polesskii, An upper bound for the reliability of information networks, Prob. Inf. Trans. 7(1971)337–339.

    Google Scholar 

  20. W.J. Myrvold, private communications (1989).

  21. L.D. Nel, Network reliability and facility location in unreliable networks, Ph.D. Thesis, University of Waterloo (1989).

  22. L.D. Nel and C.J. Colbourn, Combining Monte Carlo estimates and bounds for network reliability, Networks 20(1990)277–298.

    Google Scholar 

  23. L.D. Nel and C.J. Colbourn, Locating a broadcast facility in an unreliable network, INFOR, to appear.

  24. L.D. Nel, H.J. Strayer and C.J. Colbourn, Two-terminal bounds based on edge-packings by cutsets, Preprint (1989).

  25. V.P. Polesskii, A lower boundary for the reliability of information networks, Prob. Inf. Trans. 7(1971)165–171.

    Google Scholar 

  26. V.P. Polesskii, Obstacles to partitioning a graph into trees, Prob. Inf. Trans. 23 (3) (1987) 236–249.

    Google Scholar 

  27. J.S. Provan, The complexity of reliability computations in planar and acyclic graphs, SIAM J. Comp. 15(1986)694–702.

    Google Scholar 

  28. J.S. Provan and M.O. Ball, Computing network reliability in time polynomial in the number of cuts, Oper. Res. 32(1984)516–526.

    Google Scholar 

  29. J.S. Provan and V.G. Kulkarni, Exact cuts in networks, Networks 19(1989)281–289.

    Google Scholar 

  30. A. Ramanathan and C.J. Colbourn, Bounds on all-terminal reliability via arc-packing, Ars Combinatoria 23A(1987)229–236.

    Google Scholar 

  31. J.G. Shanthikumar, Bounding network reliability using consecutive minimal cutsets, IEEE Trans. Reliability R-37(1988)45–49.

    Google Scholar 

  32. I.A. Ushakov, New estimates of the reliability characteristics of bipolar networks, cited in [14].

    Google Scholar 

  33. I.A. Ushakov and Ye.I. Litvak, Upper and lower estimates of parameters of two-pole networks, Eng. Cybern. 15(1977)59–66.

    Google Scholar 

  34. D. Vertigan, The computational complexity of Tutte invariants for planar graphs, Preprint (1990).

  35. D.K. Wagner, Disjoint (s,t)-cuts in a network, Networks 20(1990).

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Colbourn, C.J. Combinatorial aspects of network reliability. Ann Oper Res 33, 1–15 (1991). https://doi.org/10.1007/BF02061656

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