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Among various real-life emerging applications, wireless sensor networks,Internet of Things, smart grids, social networks, communication networks,transportation networks, and computer grid systems, etc., the binary-statenetwork is the fundamental network structure and model with either working orfailed binary components. The network reliability is an effective index forassessing the network function and performance. Hence, the network reliabilitybetween two specific nodes has been widely adopted and more efficient networkreliability algorithm is always needed. To have complete information for abetter decision, all-pairs network reliability thus arises correspondingly. Inthis study, a new algorithm called the all-pairs BAT is proposed by revisingthe binary-addition-tree algorithm (BAT) and the layered-search algorithm(LSA). From both the theoretical analysis and the practical experimentsconducted on 20 benchmark problems, the proposed all-pairs BAT is moreefficient than these algorithms by trying all combinations of any pairs ofnodes.

Novel Algorithm for Computing All-Pairs Homogeneity-Arc Binary-State Undirected Network Reliability