A cut-based method for terminal-pair reliability

Terminal-pair reliability determines the probabilistic reliability between two nodes of a network, given the failure probabilities of all links. The problem has been successfully solved by the path-based partition method, network reduction technique, and the combination of the two. The path-based partition algorithm, however, requires repeated execution of a path-search procedure in an attempt to locally minimize the total number of subproblems generated. We propose a cut-based partition algorithm based on the minimum cut separating the source from the remaining network nodes. This cut-based algorithm makes no attempt to locally minimize the number of subproblems. Instead, the algorithm leads to a great reduction of the computation time for the partitioning of each subproblem. Experimental results show the superiority of the cut-based algorithm over the path-based algorithm especially for complex networks. By further employing the network reduction technique, our cut-based partition algorithm outperforms the path-based partition algorithm for all benchmarks and random sparse or dense networks. Based on the cut-based partition algorithm, we further present an incremental method of computing the terminal-pair reliability for hierarchical networks. The incremental method results in minimal recomputation of the reliability should the network configuration change.