An improved algorithm for finding all upper boundary points in a stochastic-flow network

The d-MinCut (d-MC) problem has been extensively studied in the past decades and various algorithms have been proposed. The existing algorithms often consist of two general stages, finding all the d-MC candidates and testing each candidate for being a d-MC. To find all the d-MC candidates, a system of equations and inequalities should be solved. Here, we propose a novel efficient algorithm to solve the system. Then, using our new results, an improved algorithm is proposed for the d-MC problem. Computing its complexity, we show the proposed algorithm to be more efficient than the other existing algorithms with respect to the number of minimal cuts. A medium-size network example is worked through to show how effectively the algorithm finds all the d-MCs among the set of all possible candidates in the network. Moreover, it is shown how to compute the system reliability of the example using the sum of disjoint products method. Finally, in order to illustrate the efficacy of using the new presented techniques, computational comparative results on an extensive collection of random test problems are provided in the sense of performance profile introduced by Dolan and More.