Inverse Generalized Minimum Cost Flow Problem Under the Hamming Distances

  • Mobarakeh Karimi
  • Massoud AmanEmail author
  • Ardeshir Dolati


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.


Generalized 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.


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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Mobarakeh Karimi
    • 1
  • Massoud Aman
    • 1
    Email author
  • Ardeshir Dolati
    • 2
  1. 1.Faculty of Mathematics and StatisticsUniversity of BirjandBirjandIran
  2. 2.Department of Computer ScienceShahed UniversityTehranIran

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