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Inverse Minimum Cut Problem with Lower and Upper Bounds

Author

Listed:
  • Adrian Deaconu

    (Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 50003 Brașov, Romania)

  • Laura Ciupala

    (Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 50003 Brașov, Romania)

Abstract

The inverse minimum cut problem is one of the classical inverse optimization researches. In this paper, the inverse minimum cut with a lower and upper bounds problem is considered. The problem is to change both, the lower and upper bounds on arcs so that a given feasible cut becomes a minimum cut in the modified network and the distance between the initial vector of bounds and the modified one is minimized. A strongly polynomial algorithm to solve the problem under l 1 norm is developed.

Suggested Citation

  • Adrian Deaconu & Laura Ciupala, 2020. "Inverse Minimum Cut Problem with Lower and Upper Bounds," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1494-:d:408397
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    References listed on IDEAS

    as
    1. Longcheng Liu & Jianzhong Zhang, 2006. "Inverse maximum flow problems under the weighted Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 395-408, December.
    2. Jianzhong Zhang & Mao Cai, 1998. "Inverse problem of minimum cuts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 51-58, February.
    3. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
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