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Inverse problem of minimum cuts

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Listed:
  • Jianzhong Zhang
  • Mao Cai

Abstract

Given a networkN=(V,A,c), a sources εV, a. sinkt εV and somes —t cuts and suppose each element of the capacity vectorc can be changed with a cost proportional to the changes, the inverse problem of minimum cuts we study here is to change the original capacities with the least total cost under restrictions on the changes of the capacities, so that all thoses —t cuts become minimum cuts with respect to the new capacities. In this paper we shall show that the inverse problem of minimum cuts can be directly transformed into a minimum cost circulation problem and therefore can be solved efficiently by strongly polynomial algorithms. Copyright Physica-Verlag 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:1:p:51-58
    DOI: 10.1007/BF01193836
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    References listed on IDEAS

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    1. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    2. Cai Mao-Cheng & Yanjun Li, 1997. "Inverse Matroid Intersection Problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 235-243, June.
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    Cited by:

    1. Timothy C. Y. Chan & Maria Eberg & Katharina Forster & Claire Holloway & Luciano Ieraci & Yusuf Shalaby & Nasrin Yousefi, 2022. "An Inverse Optimization Approach to Measuring Clinical Pathway Concordance," Management Science, INFORMS, vol. 68(3), pages 1882-1903, March.
    2. Zhang, Jianzhong & Liu, Zhenhong & Ma, Zhongfan, 2000. "Some reverse location problems," European Journal of Operational Research, Elsevier, vol. 124(1), pages 77-88, July.
    3. Adrian Deaconu & Laura Ciupala, 2020. "Inverse Minimum Cut Problem with Lower and Upper Bounds," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    4. Rishabh Gupta & Qi Zhang, 2022. "Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2720-2735, September.
    5. Zhang, Jianzhong & Xu, Chengxian, 2010. "Inverse optimization for linearly constrained convex separable programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 671-679, February.
    6. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1998. "Inverse optimization," Working papers WP 4003-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. M. Cai & X. Yang & Y. Li, 2000. "Inverse Problems of Submodular Functions on Digraphs," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 559-575, March.
    8. Chung, Yerim & Culus, Jean-François & Demange, Marc, 2015. "Inverse chromatic number problems in interval and permutation graphs," European Journal of Operational Research, Elsevier, vol. 243(3), pages 763-773.
    9. Timothy C. Y. Chan & Katharina Forster & Steven Habbous & Claire Holloway & Luciano Ieraci & Yusuf Shalaby & Nasrin Yousefi, 2022. "Inverse optimization on hierarchical networks: an application to breast cancer clinical pathways," Health Care Management Science, Springer, vol. 25(4), pages 590-622, December.
    10. Zhenhong Liu & Jianzhong Zhang, 2003. "On Inverse Problems of Optimum Perfect Matching," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 215-228, September.
    11. 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.
    12. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    13. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1998. "Combinatorial algorithms for inverse network flow problems," Working papers WP 4004-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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