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- W2913667721 abstract "This thesis is concerned with the determination of uniformly best reliable and worst reliable networks. The model of a network herein consists of an undirected graph G with perfectly reliable nodes and edges which may fail. The edges of G operate independently with the same probability p. The reliability, R(G,p) of G, is the probability that G is connected. A graph G$sb{rm b}$ is uniformly best reliable if R(G$sb{rm b}$,p) $geq$ R(G,p) for all G having the same number of nodes and edges as G$sb{rm b}$ and for all $rm 0 < p < 1$. A graph G$sb{rm w}$ is uniformly worst reliable if R(G$sb{rm w}$,p) $leq$ R(G,p) for all G having the same number of nodes and edges as G$sb{rm w}$ and for all $rm 0 < p < 1$.We show that the graph obtained from the removal of an independent set of edges from a complete graph, is a uniformly best reliable graph. In addition, we show that there exists a threshold graph G$sb{rm t}$ with R(G$sb{rm t}$) $leq$ R(G) for all G with the same number of nodes and edges as G and for all $rm 0 < p < 1$. This result leads to the determination of lower bounds on the reliability polynomial which may be calculated in polynomial time in the size of the network. Finally, we compare these bounds with the presently known tightest bounds of Colbourn and Harms." @default.
- W2913667721 created "2019-02-21" @default.
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- W2913667721 date "1992-01-01" @default.
- W2913667721 modified "2023-09-27" @default.
- W2913667721 title "Network bounds for edge reliability" @default.
- W2913667721 hasPublicationYear "1992" @default.
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