Network Probabilistic Connectivity: Exact Calculation with Use of Chains

The algorithmic techniques which allow high efficiency in the precise calculation of the reliability of an undirected graph with absolutely reliable nodes and unreliable edges are considered in this paper. The new variant of the branching algorithm that allow branching by chains is presented along with improvement of series-parallel reduction method that permits the reduction of a chain with more than two edges by one step. Some programming techniques which accomplish high efficiency are also discussed. Special notice is given to the problem of computer storage economy. Comprehensive computer simulation results show the advantages of the proposed algorithms, that the calculation time decreases significantly in comparison with existent methods.

[1]  A. M. Shooman.  Algorithms for network reliability and connection availability analysis , 1995, Proceedings of Electro/International 1995.

[2]  Jiandong Li,et al.  A new algorithm for network probabilistic connectivity , 1999, MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341).

[3]  Claude E. Shannon,et al.  Reliable Circuits Using Less Reliable Relays , 1956 .

[4]  Tetsushi Koide,et al.  Topological optimization with a network reliability constraint , 2001, Discret. Appl. Math..

[5]  A. Kershenbaum,et al.  Exact graph-reduction algorithms for network reliability analysis , 1991, IEEE Global Telecommunications Conference GLOBECOM '91: Countdown to the New Millennium. Conference Record.