A simple improved algorithm to find all the lower boundary points in a multiple-node-pair multistate flow network

Abstract

There are several real-world systems which can be modeled as multistate flow networks (MFNs). Many researchers have worked on reliability evaluation of an MFN, and accordingly variety of approaches have been proposed in this regard. The problem of finding all the lower boundary points (LBPs) in a multistate flow network (MFN) has been attracting significant attention in the recent decades as these vectors can be used for reliability evaluation of MFNs. Once all the LBPs are determined, the reliability of the network can be calculated by using some techniques such as the inclusion–exclusion principle or the sum of disjoint products (SDP). Several algorithms have been proposed to address this problem in the literature in terms of minimal paths or minimal cuts. As in the real systems the data (flow or commodity) are usually transmitting from several sources to a number of destinations, the problem of determining all the LBPs in a multi-node-pair MFN is considered in this work. An improved algorithm is proposed to address the problem. The algorithm is illustrated through a benchmark network example. The complexity results are computed. The efficiency of the algorithm is demonstrated through a numerical example and the complexity results.