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Speeding up computation of the reliability polynomial coefficients for a random graph

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Abstract

We consider the problem of computing the coefficients of the reliability polynomial (RP) for a random graph with reliable vertices and unreliable edges. To speed up the computation, we use the meaning of RP coefficients in one of its representations and prove vector relations over vectors of binomial coefficients.

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References

  1. Rodionova, O.K., Rodionov, A.S., and Choo, H., Network Probabilistic Connectivity: Exact Calculation with Use of Chains, Proc. ICCSA-2004, Lect. Notes Comp. Sci., 1904, vol. 3046, pp. 315–324.

    Google Scholar 

  2. Krivoulets, V.G. and Polesskii, V.P., What is the Theory of Bounds for Network Reliability?, Inf. Processes, 1901, vol. 1, no. 2, pp. 199–203.

    Google Scholar 

  3. Lucet, C. and Manouvrier, J.-F., Exact Methods to Compute Network Reliability, Proc. 1st Int. Conf. on Mathematical Methods in Reliability, Bucharest, 1997, available from http://ramp.ucsd.edu/resources. html.

  4. Satyanarayana, A. and Chang, M.K., Network Reliability and the Factoring Theorem, Networks, 1983, vol. 13, pp. 107–120.

    Article  MATH  MathSciNet  Google Scholar 

  5. Shooman, A.M., Algorithms for Network Reliability and Connection Availability Analysis, Proc. Electro/95 Int. Professional Program, 1995, pp. 309–333.

  6. Ayanoglu, E. and Chih-Lin, I., A Method of Computing the Coefficients of the Network Reliability Polynomial, Proc. GLOBECOM’89, IEEE, 1989, vol. 1, pp. 331–337.

    Google Scholar 

  7. Colbourn, C.J., Some Open Problems on Reliability Polynomials, Congr. Numer., 1993, vol. 93, pp. 187–202.

    MATH  MathSciNet  Google Scholar 

  8. Chari, M. and Colbourn, C.J., Reliability Polynomials: A Survey, Combin. Inform. Syst. Sci., 1997, vol. 22, pp. 177–193.

    MATH  MathSciNet  Google Scholar 

  9. Page, L.B. and Perry, J.E., Reliability Polynomials and Link Importance in Networks, IEEE Trans. Reliab., 1994, vol. 43, no. 1, pp. 51–58.

    Article  Google Scholar 

  10. Rodionova, O.K., Rodionov, A.S., and Choo, H., Network Probabilistic Connectivity: Optimal Structures, Proc. ICCSA-2004, LNCS, 1904, vol. 3047, pp. 431–440.

    Google Scholar 

  11. Gertsbakh, I. and Shpungin, Y., Network Rreliability Importance Measures: Combinatorics and Monte Carlo Based Computations, WSEAS Trans. Computers Archive, 1908, vol. 7, no. 4, pp. 216–227.

    Google Scholar 

  12. Rodionova, O.K., PPP GRAPH-ES/1. Connectivity of Multigraphs with Unreliable Edges (Atlas, Procedures), Preprint of Computing Center, Siberian Branch, USSR Acad. Sci., Novosibirsk, 1982.

  13. Camarda, P., Bounds Evaluation of Coefficients in the Reliability Polynomial, Microelectr. Reliab., 1990, vol. 30, no. 2, pp. 1099–1110.

    Article  Google Scholar 

  14. Rodionov, A.S., Rodionova, O.K., and Choo, H., Network Probabilistic Connectivity: Reliability Polynomial, ISPC Communication-2004, Proc. 8th Int. Conf. “Problems of Operation of Information Networks,” 2004, vol. 1, pp. 321–327.

    Google Scholar 

  15. Rodionov, A.S., Rodionova, O.K., Migov, D.A., and Murzin, M.Yu., Using the Branching Method for Exact Computation of the Connectivity Probability of a Random Graph, in Matematika i bezopasnost’ informatsionnykh tekhnologii (Mathematics and Security of Information Technologies), Moscow: MTsNMO, 1905, pp. 141–146.

    Google Scholar 

  16. Rodionov, A.S. and Rodionova, O.K., The Branching Method for the Computation of Connectivity Characteristics of Networks, Vest. SibGUTI, 1907, pp. 63–66.

  17. Rodionov, A.S., Using the Meaning of Reliability Polynomial Coefficients of a Random Graph to Speed up Their Computation, Mat. X mezhdunar. konf. “Problemy funktsionirovaniya informatsionnykh setei” (Proc. X Int. Conf. “Problems of Informational Networks Operation”), Novosibirsk: IVMiMG SO RAN, 1908, pp. 129–134.

    Google Scholar 

  18. Cvetkovic, D.M., Doob, M., and Sachs, H., Spectra of Graphs: Theory and Applications, Heidelberg: Johann Ambrosius Barth Verlag, 1995, 3rd ed.

    MATH  Google Scholar 

  19. Rodionov, A.S. and Rodionova, O.K., On Exact Computation of Graph Connectivity Probability, Tr. mezhdunar. konf. “Vychislitel’nye tekhnologii i matematicheskie modeli v nauke, tekhnike i obrazovanii” (Proc. Int. Conf. “Computational Technologies and Mathematical Models in Science, Technics, and Education”), Alma-Ata, 1902, vol. 5, pp. 140–147.

    Google Scholar 

  20. Migov, D.A., Connectivity Probability for a 5-vertex Graph, Mater. mezhdunar. seminara “Vychislitel’nye metody i reshenie optimizatsionnykh zadach” (Proc. Int. Seminar “Computational Methods and Solving Optimizational Problems”), Novosibirsk, 1904, pp. 113–116.

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  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    A. S. Rodionov

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  1. A. S. Rodionov
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Original Russian Text © A.S. Rodionov, 2011, published in Avtomatika i Telemekhanika, 2011, No. 7, pp. 134–146.

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Rodionov, A.S. Speeding up computation of the reliability polynomial coefficients for a random graph. Autom Remote Control 72, 1474–1486 (2011). https://doi.org/10.1134/S0005117911070150

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