Abstract
We consider the problem of reliability calculation of networks with diameter constraint. It is assumed that the network has unreliable communication links and perfectly reliable nodes. The diameter constrained reliability (DCNR) for such network is defined as a probability that every pair of terminals of network is connected by operational paths with a number of included edges less or equal to a given integer. The problem of computing this characteristic is known to be NP-hard, just like the problem of computing the probability of network connectivity. We propose new methods of speeding up of DCNR calculation. These methods are the edge reduction and the edge selection strategy for DCNR computing by the well-known factoring method. Also, we propose the parallel method for DCNR calculation and the method of cumulative updating of lower and upper bounds of DCNR, which allows to decide the feasibility of a network with respect to given threshold without performing exhaustive calculation of reliability. Experiments show an applicability of proposed methods.
Supported by Russian Foundation for Basic Research under grants 14-07-31069, 13-07-00589.
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References
Ball, M.O.: Computational complexity of network reliability analysis: An overview. IEEE Transactions on Reliability 35, 230–239 (1986)
Shooman, A.M., Kershenbaum, A.: Exact graph-reduction algorithms for network reliability analysis. In: IEEE Global Telecommunications Conference GLOBECOM 1991, pp. 1412–1420. IEEEP Press, New York (1991)
Rodionova, O.K., Rodionov, A.S., Choo, H.: Network probabilistic connectivity: exact calculation with use of chains. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCSA 2004. LNCS, vol. 3036, pp. 565–568. Springer, Heidelberg (2004)
Migov, D.A., Rodionova, O.K., Rodionov, A.S., Choo, H.: Network probabilistic connectivity: using node cuts. In: Zhou, X., et al. (eds.) EUC Workshops 2006. LNCS, vol. 4097, pp. 702–709. Springer, Heidelberg (2006)
Xiao, Y.: An Efficient Network Reliability Computation Method Based on Isomorphism Judgment. Journal of Networks 9(8), 2037–2044 (2014)
Forghani-elahabad, M., Mahdavi-Amiri, N.: A New Efficient Approach to Search for All Multi-State Minimal Cuts. IEEE Trans. on Reliability 63(1), 154–166 (2014)
Migov, D.A., Rodionov, A.S.: Parallel implementation of the factoring method for network reliability calculation. In: Murgante, B., et al. (eds.) ICCSA 2014, Part VI. LNCS, vol. 8584, pp. 654–664. Springer, Heidelberg (2014)
Pandurangan, G., Raghavan, P., Upfal, E.: Building Low-Diameter Peer-to-Peer Networks. IEEE Journal on Selected Areas in Communications (JSAC) 21(6), 995–1002 (2003)
Petingi, L., Rodriguez, J.: Reliability of Networks with Delay Constraints. Congressus Numerantium 152, 117–123 (2001)
Cancela, H., Petingi, L.: Diameter constrained network reliability: exact evaluation by factorization and bounds. In: Int. Conf. on Industrial Logistics, Okinawa, Japan, pp. 359–356 (2001)
Cancela, H., Robledo, F., Rubino, G., Sartor, P.: Monte Carlo Estimation of Diameter Constrained Network Reliability Conditioned by Pathsets and Cutsets. Computer Communications 36(6), 611–620 (2013)
Jin, R., Liu, L., Ding, B., Wang, H.: Distance-Constraint Reachability Computation in Uncertain Graphs. In: VLDB Endowment, vol. 4, pp. 551–562 (2011)
Migov, D.A.: Computing Diameter Constrained Reliability of a Network with Junction Points. Automation and Remote Control 72(7), 1415–1419 (2011)
Canale, E., Cancela, H., Robledo, F., Rubino, G., Sartor, P.: On Computing the 2-Diameter-Constrained K-Reliability of Networks. International Transactions in Operational Research 20(1), 49–58 (2013)
Won, J.-M., Karray, F.: Cumulative Update of All-Terminal Reliability for Faster Feasibility Decision. IEEE Trans. on Reliability 59(3), 551–562 (2010)
Won, J.-M., Karray, F.: A Greedy Algorithm for Faster Feasibility Evaluation of All-Terminal-Reliable Networks. IEEE Trans. on Systems, Man, and Cybernetics, Part B Cybernetics 41(6), 1600–1611 (2011)
Rodionov, A.S., Migov, D.A., Rodionova, O.K.: Improvements in the Efficiency of Cumulative Updating of All-Terminal Network Reliability. IEEE Trans. on Reliability 61(2), 460–465 (2012)
Nechunaeva, K.A., Migov, D.A.: Speeding up of genetic algorithm for network topology optimization with use of cumulative updating of network reliability. In: ACM IMCOM 2015, article 42, ACM New York (2015)
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Migov, D.A., Nesterov, S.N. (2015). Methods of Speeding up of Diameter Constrained Network Reliability Calculation. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9156. Springer, Cham. https://doi.org/10.1007/978-3-319-21407-8_9
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DOI: https://doi.org/10.1007/978-3-319-21407-8_9
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