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This paper presents an efficient cutset approach to compute the reliability of a large communication network having heterogeneous link capacities. The reliability measure has been defined as capacity related reliability (CRR). The proposed method, subset cut technique (SCT), requires the cutset information of the network. For each minimal cut Ci, and a given minimum bandwidth requirement Wmin, the method enumerates all nonredundant subset cut (SC), where each SC relates link capacities & minimum bandwidth requirements. Note that if all links in an SC fail, the capacity of the induced cut Ci will be less than Wmin. Given the failure probability of each link, and the nonredundant SC, any Boolean technique for generating mutually disjoint terms can be utilized to obtain a capacity related unreliability (CRU) of the network. Thus, the CRU for an (s,t) node pair is the probability that the network has a capacity of less than Wmin for the given node pair. Note that CRR=1-CRU. Two SCT algorithms are proposed: Algorithm-1, and Algorithm-2; and the suitability of using either algorithm is also discussed. Examples are given to illustrate the techniques. The time complexity, and the proof of correctness for the proposed algorithms are also included. It is shown empirically that the time complexity of generating the nonredundant SC of a network is polynomial in the order of the number of cuts of the network. The proposed SCT algorithms have been implemented in C. We have utilized the SCT to generate the CRR of some large communication networks with various Wmin values.