Computing optimal assignments for residual network reliability Original Research Article

We study the problem of assigning given failure probabilities to the nodes of a network so as to optimize its reliability. The measure used is the residual node connectedness reliability of the network, which is defined as the probability that the operating nodes are connected. In this paper, we show how optimal assignments can be found in polynomial time for paths, cycles, threshold graphs, and complete graphs minus a matching. On the other hand, the problem is shown to be NP-hard even for complete bipartite graphs.