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Inverse minimum flow problem

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Abstract

In this paper we consider the inverse minimum flow (ImF) problem, where lower and upper bounds for the flow must be changed as little as possible so that a given feasible flow becomes a minimum flow. A linear time and space method to decide if the problem has solution is presented. Strongly and weakly polynomial algorithms for solving the ImF problem are proposed. Some particular cases are studied and a numerical example is given.

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References

  1. R. K. Ahuja, T. L. Magnanti and J. B. Orlin,Network flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, NJ, 1993.

    Google Scholar 

  2. R. K. Ahuja and J. B. Orlin,A Faster Algorithm for the Inverse Spanning Tree Problem, Journal of Algorithms34 (2000), 177–193.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. K. Ahuja and J. B. Orlin,Combinatorial Algorithms for Inverse Network Flow Problems, Sloan School of Management, MIT, Cambridge, MA, sent for publication, 1998.

    Google Scholar 

  4. R. K. Ahuja and J. B. Orlin,Inverse Optimization, Working Paper, Sloan School of Management, MIT, Cambridge, MA, 1998.

    Google Scholar 

  5. D. Burton, B. Paulleyblank and Ph. L. Toint,The inverse shortest paths problem with upper bounds on shortest paths costs, Network Optimization (P. Pardalos, D. W. Hearn and W. H. Harger), Lecture Notes in Econom, Math. Systems, vol. 450, pp. 156–171, Springer-Verlang, Berlin/New York, 1997.

    Google Scholar 

  6. D. Burton and Ph. L. Toint,On an Instance of the Inverse Shortest Path Problem, Math. Programming53 (1992), 45–61.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Burton and Ph. L. Toint,On the Use of an Inverse Shortest Path Algorithm for Recovering Linearly Correlated Costs, Math. Programming63 (1994), 1–22.

    Article  MathSciNet  Google Scholar 

  8. M. Cai and X. Yang,Inverse Shortest Path Problems, Technical Report, Institute of Systems Sciences, Academia Sinica, Beijing, China, 1994.

    Google Scholar 

  9. E. Ciurea and L. Ciupala,Sequential and Parallel Algorithms for Minimum Flows, J. Appl. Math. & Computing15(1–2) (2004), 53–75.

    MATH  MathSciNet  Google Scholar 

  10. C. Heuberger,Inverse Combinatorial Optimization: A Survey on Problems, Methods and Results, Journal of Combinatorial Optimization8 (2004), 329–361.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Huang and Z. Liu,On the Inverse Version of the Minimum Cost Flow Problem, Mathematical Programming33, 187–203.

  12. P. T. Sokkalingam, R. K. Ahuja and J. B. Orlin,Solving Inverse Spanning Tree Problems through Network Flow Techniques, Oper. Res.47 (1999), 291–298.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Yang and J. Zhang,Inverse Maximum Capacity Path with Upper Bound Constraints, OR Spektrum.

  14. C. Yang, J. Zhang and Z. Ma,Inverse Maximum Flow and Minimum Cut Problems, Optimization40 (1997), 147–170.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Zhang and C. Cai,Inverse Problems of Minimum Cuts, ZOR-Math. Methods Oper. Res.48 (1998), 51–58.

    Article  MathSciNet  Google Scholar 

  16. J. Zhang, Z. Liu and Z. Ma,On the Inverse Problem of Minimum Spanning Tree with Partition Constrains, Math. Methods Oper. Res.44 (1996), 171–188.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Zhang, Z. Ma and C. Yang,A Column Generation Method for Inverse Shortest Path Problems, ZOR-Math. Methods Oper. Res.41 (1995), 347–358.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Computer Science, Transilvania University, str. Iuliu Maniu nr. 50, Brasov, Romania

    Eleonor Ciurea & Adrian Deaconu

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  1. Eleonor Ciurea
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  2. Adrian Deaconu
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Correspondence to Eleonor Ciurea.

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Ciurea, E., Deaconu, A. Inverse minimum flow problem. J. Appl. Math. Comput. 23, 193–203 (2007). https://doi.org/10.1007/BF02831968

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  • DOI: https://doi.org/10.1007/BF02831968

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