Abstract
An inverse optimization problem is defined as follows: Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost (capacity) vector , and x 0 ∈ S. We want to perturb the cost (capacity) vector c to d such that x 0 becomes an optimal solution of P with respect to the cost (capacity) vector d, and to minimize some objective functions. In this paper, we consider the weighted inverse minimum cut problem under the sum-type Hamming distance. First, we show the general case is NP-hard. Second we present a combinatorial algorithm that run in strongly polynomial time to solve a special case.
This research is supported by the National Natural Science Foundation of China (Grant No. 11001232), Fundamental Research Funds for the Central Universities (Grant No. 2010121004) and Department of Education of Zhejiang Province of China (Grant No. Y200909535).
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Liu, L., Chen, Y., Wu, B., Yao, E. (2012). Weighted Inverse Minimum Cut Problem under the Sum-Type Hamming Distance. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_3
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DOI: https://doi.org/10.1007/978-3-642-29700-7_3
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