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- W2893205929 abstract "Let us model the network by an undirected graph G, in which each edge fails independently with probability q∈[0,1], the all-terminal reliability of the network is the probability that the graph G remains connected and it is one of the important measure for the invulnerability of the network. Clearly, the all-terminal reliability can be written as a polynomial in either q. Theoretically, it has been proved that calculating all-terminal reliability for planar networks is #P-complete. Up now we cannot find any results for some special classes of the planar networks. This paper studies the all-terminal reliability of the two-tree networks and its generalizations. A linear algorithm for calculating the reliability of a planar two-tree networks is proposed, with algorithmic complexity O(n), where n is the number of steps. Then both the uniformly-most reliable network model and the uniformly-worst reliable network model are determined by using the algorithm. Finally, a polynomial algorithm for planar two-connected networks is proposed based on an expended algorithm and the corresponding uniformly-most reliable network model and uniformly-worst reliable network model are also presented, with computational complexity O(n), where n is the number of steps." @default.
- W2893205929 created "2018-10-05" @default.
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- W2893205929 date "2019-05-01" @default.
- W2893205929 modified "2023-10-18" @default.
- W2893205929 title "Invulnerability of planar two-tree networks" @default.
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- W2893205929 doi "https://doi.org/10.1016/j.tcs.2018.09.021" @default.
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