An Algorithm to Search for All Minimal Cuts in a Flow Network

Abstract

Reliability evaluation approaches exploit a variety of tools for system modeling and calculation of reliability indices. Most proposed approaches in the literature are in terms of minimal cuts (MCs) or minimal paths. Hence, finding all the MCs in a network is an attractive problem in network flow and reliability theory. Here, investigating some works related to the MC problem, we first point out a number of defects in certain proposed algorithms, and present certain new techniques to rectify the flaws in two algorithms. Moreover, we present some techniques to improve the algorithms. Using our results, we propose an improved algorithm for finding all the MCs in a flow network. A benchmark network example is used to illustrate the performance of the algorithm. The proposed algorithm is shown to be correct. Finally, after establishing the complexity results, we demonstrate the proposed algorithm to be more efficient than some existing algorithms.