Search for all d-Mincuts of a limited-flow network

Abstract

In this presentation, we developed an intuitive algorithm based on some simple concepts that were found in this study. It is more efficient than the best-known existing algorithm. The computational complexity of the proposed algorithm is analyzed and compared with the existing methods. One example is illustrated to show how all d-MCs are generated by our proposed algorithm. As evidence of the utility of the proposed approach, extensive computational results on random test problems are presented. Our results compare favorably with previously developed algorithms in the literature. Scope and purpose Many real-world systems are multistate systems composed of multistate components in which the reliability can be computed in terms of the lower bound points of level d, called d-Mincuts ( d-MCs). Such systems (electric power, transportation, etc.) may be regarded as flow networks whose arcs have independent, discrete, limited and multivalued random capacities. In this study, all MCs are assumed to be known in advance and we focused on how to find the entire d-MCs before calculating the reliability value of a network. Analysis of our algorithm and comparison to existing algorithms shows that our proposed method has the following advantages: (1) the number of d-MC candidates is less than those in the existing methods, (2) the d-MC candidates are simpler to find and verify, which makes the method more effective than the existing methods, and (3) our method is easier to understand and implement.