In Nature, the primary goal of any network is to survive. This is less obvious for engineering networks (electric power, gas, water, transportation systems etc.) that are expected to operate under normal conditions most of time. As a result, the ability of a network to withstand massive sudden damage caused by adverse events (or survivability) has not been among traditional goals in the network design. Reality, however, calls for the adjustment of design priorities. As modern networks develop toward increasing their size, complexity, and integration, the likelihood of adverse events increases too due to technological development, climate change, and activities in the political arena among other factors. Under such circumstances, a network failure has an unprecedented effect on lives and economy. To mitigate the impact of adverse events on the network operability, the survivability analysis must be conducted at the early stage of the network design. Such analysis requires the development of new analytical and computational tools. Computational analysis of the network survivability is the exponential time problem at least. The current paper describes a new algorithm, in which the reduction of the computational complexity is achieved by mapping an initial network topology with multiple sources and sinks onto a set of simpler smaller topologies with multiple sources and a single sink. Steps for further reducing the time and space expenses of computations are also discussed.