Inverse Generalized Minimum Cost Flow Problem Under the Hamming Distances
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Given a generalized minimum cost flow problem, the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem. In this paper, we consider both types of the weighted Hamming distances for measuring the adjustment. In the sum-type case, it is shown that the inverse problem is APX-hard. In the bottleneck-type case, we present a polynomial time algorithm.
KeywordsGeneralized minimum cost flow Inverse problem Hamming distance Binary search
We thank the anonymous referees for giving valuable comments and suggestions to improve the presentation of this paper.