A New Efficient Approach to Search for All Multi-State Minimal Cuts

An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint

“…To identify and remove a duplicate, below we show how to use a data structure recently proposed by Forghani-elahabad and Mahdavi-Amiri [21].…”

“…We know r þ 1 is the number of all the Γ vectors obtained by using Lemma 3. Hence, the time complexity of using the data structure provided in [21] for removing the duplicate vectors is Oðr log ðrÞÞ. Now that we know how to determine the policy vectors, calculate the corresponding state vectors, and remove the nonminimal vectors and of course the duplicate minimal ones, we are at a position to present our algorithm.…”

“…For this purpose, any one of the algorithms proposed in the literature [40,41] can be employed. In Algorithm 1 below, we use Technique 1 in Step 1 to find the policy vectors satisfying the budget constraint, Lemma 3 in Step 2 to determine the Γ vectors, the data structure proposed in [21] in Step 3 to remove the duplicates, Theorem 1 in Step 4 to remove the non-minimal ones, and System (2) in Step 5 to determine system state vectors. Input: A stochastic-flow network with two separate minimal paths, demand level d, time limitation T, and budget constraint b.…”

“…In an SFN, system reliability can be considered as the probability of transmitting a given demand amount, d units, of data (flow) from a source node to a sink node . A number of different algorithms have been proposed to compute this kind of reliability parameter [3,[13][14][15][16][17][18][19][20][21]. For example, Yan and Qian [19] presented several new results along with an improved algorithm.…”

“…For example, Yan and Qian [19] presented several new results along with an improved algorithm. Forghani-elahabad and Mahdavi-Amiri [21] proposed a new data structure and established some new results to present a new efficient algorithm. However, in an optical network, there are some time thresholds and when the transmission time exceeds the threshold, the transmission will be canceled, and so the transmission time is an important issue to be considered.…”