A Novel Algorithm for All Minimal Cut Vectors Without Duplicates in Two-Terminal Multistate Networks

Multistate networks (MFNs) play an important role in many modeling real-world systems, and the reliability of these networks is often evaluated using minimal cut vectors, namely <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex>-MCs. However, existing algorithms for searching <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex>-MCs require an additional post hoc step to detect and eliminate duplicate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex>-MCs, which require timeconsuming post-processing, significantly impacting algorithmic efficiency. This article focuses on this problem and presents new theoretical findings to improve its solution. Based on these results, a new algorithm is proposed to identify and prevent duplicate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex>-MCs. The time complexity and computational experiments demonstrate the superior performance of the proposed algorithm compared with reported algorithms.