Data for the article A New Efficient Algorithm Addressing the (d, c)-MC Problem

Many real-world systems can be modeled by multistate flow networks (MFNs) and their reliability evaluation features in designing and control of these systems. Considering the cost constraint makes the problem of reliability evaluation of an MFN more realistic. For a given demand value $d$ and a given cost limit $c$, the reliability of an MFN at level $(d, c)$ is the probability of transmitting at least $d$ units from the source node to the sink node through the network within the cost of $c$. This article addresses this so-called $(d, c)$-MC problem in terms of minimal cuts. It presents new results on which a new algorithm is based. This algorithm finds all $(d, c)$-MC candidates without duplicates and verifies them more efficiently than existing ones. The complexity results for this algorithm and an example of its use are provided. Finally, numerical experiments with R implementations of the presented algorithm and other competitive algorithms are considered. Both, the time complexity analysis and numerical experiments demonstrate the presented algorithm to be more efficient than other existing ones in the majority of cases.