A New Node-Based Algorithm for Identifying the Complete Minimal Cut Set

Abstract

The binary-state network, which is fundamental to several modern systems, only operates in two states: operational or inoperable. Network reliability is crucial in its planning, design, and evaluation, with the minimal cut (MC) being a cornerstone for reliability algorithms. A recursive binary-addition-tree algorithm (BAT) excels in its capacity to promptly eliminate infeasible vectors. However, it relies on a depth-first search (DFS), a technique surpassed in efficiency by BAT. To the best of our knowledge, no exploration into a recursive MC-based BAT for MC identification has been undertaken thus far. Therefore, this manuscript introduces the recursive node-based BAT, devised such that the ith iteration of the jth vector mirrors its progenitor vector, barring its ith coordinate valued at one. This BAT method, paired with rules to eliminate infeasible vectors, demonstrates high efficiency in deriving MCs. This is evident in the time complexity analysis and tests on 20 benchmark binary-state networks. A thorough examination of the empirical findings highlights the distinctive features and benefits of the proposed approach. Specifically, the strategic reordering of node numbers, along with the isolated nodes concept, significantly reduces the occurrence of infeasible vectors. Simultaneously, the inclusion of edge nodes expedites the feasibility verification process for vectors. Ultimately, the proposed recursive node-based BAT algorithm framework ensures a more efficient process for generating vectors.