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Algorithms for the partial inverse matroid problem in which weights can only be increased

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Abstract

In a partial inverse combinatorial problem, given a partial solution, the goal is to modify data as small as possible such that there exists an optimal solution containing the given partial solution. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be increased. Two polynomial time algorithms are presented for this problem.

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References

  1. Ahuja, R.K., Orlin, J.B.: Inverse optimization. Oper. Res. 49(5), 771–783 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Burton, D., Toint, P.L.: On an instance of the inverse shortest path problem. Math. Program. 53, 45–61 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cai, M., Duin, C.W., Yang, X., Zhang, J.: The partial inverse minimum spanning tree problem when weight increase is forbidden. Eur. J. Oper. Res. 188, 348–353 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. DellAmico, M., Maffioli, F., Malucelli, F.: The base-matroid and inverse combinatorial optimization problems. Discrete Appl. Math. 128, 337–353 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Demange, M., Monnot, J.: An introduction to inverse combinatorial problems. In: Paschos, V.T. (ed.) Paradigms of Combinatorial Optimization (Problems and New approaches). Wiley, London (2010)

    Google Scholar 

  6. Floudas, C.A., Pardalos, P.M. (eds.): Encyclopedia of optimization. Springer, New York (2009)

  7. Frank, A.: A weighted matroid intersection algorithm. J. Algorithm 2, 328–336 (1981)

  8. Gassner, E.: Selected Partial Inverse Combinatirial Optimization Problems with Forbidden Elements. Technical Report 2009-15, Graz University of Technology (2009)

  9. Gassner, E.: The partial inverse minimum cut problem with \(L_{1}\)-norm is strongly NP-hard. RAIRO Oper. Res. 44, 241–249 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gentry, S.: Partial Inverse Linear Programming. MIT Lab for Information and Decision Systems Report, LIDS-P-2532 (2001)

  11. Heuberger, C.: Inverse optimization: a survey on problems, methods, and results. J. Combin. Optim. 8, 329–361 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lai, T., Orlin, J.: The Complexity of Preprocessing. Research Report of Sloan School of Management. MIT (2003)

  13. Moser, T.J.: Shortest paths calculation of seismic rays. Geophysics 56, 59–67 (1991)

    Article  Google Scholar 

  14. Oxley, J.G.: Matroid Theory. Oxford University Press, Oxford (1992)

    MATH  Google Scholar 

  15. Pitsoulis, L.S.: Topics in matroid theory. Springer, New York (2014)

  16. Wang, Q.: Partial inverse most unbalanced spanning tree problem. Prz. Elektrotech. 88(1b), 111–114 (2012)

    Google Scholar 

  17. Yang, X.: Robust partial inverse network flow problems. Appl. Math. J. Chin. Univ. Ser. B 16(2), 185–194 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang, X.: Complexity of partial inverse assignment problem and partial inverse cut problem. RAIRO Oper. Res. 35, 117–126 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yang, X., Zhang, J.: Partial inverse assignment problems under \(l_1\) norm. Oper. Res. Lett. 35, 23–28 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang, X., Zhang, J.: Inverse sorting problem by minimizing the total weighted number of changes and partial inverse sorting problems. Comput. Optim. Appl. 36, 55–66 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This research is supported by NSFC (61222201, 11531011), SRFDP (20126501110001), and Xingjiang Talent Youth Project (2013711011).

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Authors and Affiliations

  1. College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Zhao Zhang

  2. College of Mathematics and System Sciences, Xinjiang University, Ürümqi, 830046, Xinjiang, China

    Shuangshuang Li

  3. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA

    Hong-Jian Lai

  4. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Ding-Zhu Du

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  1. Zhao Zhang
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  2. Shuangshuang Li
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  3. Hong-Jian Lai
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  4. Ding-Zhu Du
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Correspondence to Zhao Zhang.

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Zhang, Z., Li, S., Lai, HJ. et al. Algorithms for the partial inverse matroid problem in which weights can only be increased. J Glob Optim 65, 801–811 (2016). https://doi.org/10.1007/s10898-016-0412-x

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  • DOI: https://doi.org/10.1007/s10898-016-0412-x

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