Skip to main content
SpringerLink
Log in

A note on boundingk-terminal reliability

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

A generalization of a theorem of Lomonosov and Polesskii is proved, which provides a novel method for determining upper bounds on the probability that a graph contains a Steiner tree (k-terminal reliability).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. M. F. AboElFotoh and C. J. Colbourn, Series-parallel bounds for the two-terminal reliability problem,ORSA J. Comput. 1 (1989), 209–222.

    MATH  Google Scholar 

  2. M. O. Ball and J. S. Provan, Bounds on the reliability polynomial for shellable independence systems,SIAM J. Algebraic Discrete Methods 3 (1982), 166–181.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. J. Colbourn,The Combinatorics of Network Reliability, Oxford University Press, Oxford, 1987.

    Google Scholar 

  4. C. J. Colbourn, Edge-packings of graphs and network reliability,Discrete Math. 72 (1988), 49–61.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. J. Colbourn, The combinatorics of network reliability: an update,Proc. NATO Advanced Research Workshop on Topological Network Design, Copenhagen, 1989.

  6. R. E. Gomory and T. C. Hu, Multiterminal network flows,SIAM J. Appl. Math. 9 (1961), 551–570.

    Article  MATH  MathSciNet  Google Scholar 

  7. R. M. Karp, Reducibility among combinatorial problems, in:Complexity of Computer Computations (R. E. Miller, J. W. Thatcher, eds) Plenum, New York, 1972, pp. 85–103.

    Google Scholar 

  8. M. V. Lomonosov, Bernoulli scheme with closure,Problems Inform. Transmission 10 (1974), 73–81.

    MathSciNet  Google Scholar 

  9. M. V. Lomonosov and V. P. Polesskii, An upper bound for the reliability of information networks,Problems Inform. Transmission 7 (1971), 337–339.

    MathSciNet  Google Scholar 

  10. J. S. Provan and M. O. Ball, The complexity of counting cuts and of computing the probability that a graph is connected,SIAM J. Comput. 12 (1983), 777–788.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. G. Valiant, The complexity of enumeration and reliability problems,SIAM J. Comput. 8 (1979), 410–421.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Charles J. Colbourn

Authors
  1. Charles J. Colbourn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by F. K. Hwang.

This research was supported by NSERC Canada under Grant No. A0579.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colbourn, C.J. A note on boundingk-terminal reliability. Algorithmica 7, 303–307 (1992). https://doi.org/10.1007/BF01758764

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01758764

Key words

Search

Navigation