Irredundant Subset Cut Generation to Compute Capacity Related Reliability

This paper proposes an efficient cut set approach to enumerate the subsets cut groups (SCG) from apriori knowledge of minimal cutsets of a network. These SCG block a given amount of flow through the network despite the network being (s, t) connected and are being used to evaluate capacity related reliability (CRR) by employing any sum of disjoint product approach. For each minimal cutset and a given flow requirement, the proposed method enumerates the non-redundant SCG from a cut-matrix, which is constructed from the minimal cutsets information. Two simple equations are proposed to check the validity of a cut for being (i) valid SCG (as a whole) or (ii) used to enumerate its subsets from a certain order onwards to form valid SCG. Thus, an enumeration scheme to enumerate subsets of certain order from a given set is also proposed. The proposed approach is illustrated with an example and implemented using MATLAB. Several examples are solved and their results are also provided along with a comparison with recent algorithms.