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Inverse Generalized Minimum Cost Flow Problem Under the Hamming Distances

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Abstract

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.

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Acknowledgements

We thank the anonymous referees for giving valuable comments and suggestions to improve the presentation of this paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran

    Mobarakeh Karimi & Massoud Aman

  2. Department of Computer Science, Shahed University, Tehran, Iran

    Ardeshir Dolati

Authors
  1. Mobarakeh Karimi
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  2. Massoud Aman
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  3. Ardeshir Dolati
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Correspondence to Massoud Aman.

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Karimi, M., Aman, M. & Dolati, A. Inverse Generalized Minimum Cost Flow Problem Under the Hamming Distances. J. Oper. Res. Soc. China 7, 355–364 (2019). https://doi.org/10.1007/s40305-018-0231-5

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  • DOI: https://doi.org/10.1007/s40305-018-0231-5

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