en Discrete Optimization Discrete Optimization پژوهشی Original <p>Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capacity inverse problem under the bottleneck-type and the sum-type weighted Hamming distances. In the bottleneck-type case, the binary search technique is applied to present an algorithm for solving the problem in O(nm log n) time. In the sum-type case, it is shown that the inverse problem is strongly NP-hard even on bipartite networks</p> Combinatorial optimization, minimum cost flow problem, inverse problem, Hamming distance, complexity 0 0 http://iors.ir/journal/browse.php?a_code=A-10-520-2&slc_lang=en&sid=1 M Aman mamann@birjand.ac.ir 00031947532846001395 00031947532846001395 No Mathematics Department J Tayyebi javadtayyebi@birjand.ac.ir 00031947532846001396 00031947532846001396 Yes Mathematics Department