Advertisement

Inverse Bottleneck Optimization Problems on Networks

  • Xiucui Guan
  • Jianzhong Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)

Abstract

The bottleneck optimization problem is to find a feasible solution that minimizes the bottleneck cost. In this paper, we consider the inverse bottleneck optimization problems with bound constraints on modification under weighted l 1 norm, weighted sum-Hamming distance and weighted bottleneck-Hamming distance. That is, given a feasible solution F *, we aim to modify the cost function under some measure such that F * becomes an optimal solution to the bottleneck optimization problem. We show that the inverse problem under weighted l 1 norm and weighted sum-Hamming distance can be reduced to O(m) minimum cut problems, while the inverse problem under weighted bottleneck-Hamming distance can be reduced to O(logm) cut feasibility problems, where m = |E|.

Keywords

Inverse Problem Feasible Solution Span Tree Problem Capacity Vector Isotonic Regression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cai, M., Yang, X., Zhang, J.: The complexity analysis of the inverse center location problem. J. Global Optim. 5, 213–218 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Duin, C.W., Volgenant, A.: Some inverse optimization problems under the Hamming distance. European J. Oper. Res. 170, 887–899 (2006)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Guan, X., Zhang, J.: Inverse Constrained Bottleneck Problems Under Weighted l  ∞  Norm. Comput. and Oper. Res., Available online (February 2, 2006)Google Scholar
  4. 4.
    Heuberger, C.: Inverse optimization, a survey on problems, methods, and results. J. Comb. Optim. 329, 329–361 (2004)CrossRefMathSciNetGoogle Scholar
  5. 5.
    He, Y., Zhang, B., Yao, E.: Weighted Inverse Minimum Spanning Tree Problems under Hamming Distance. J. Comb. Optim. 9, 91–100 (2005)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    He, Y., Zhang, B., Zhang, J.: Constrained Inverse Minimum Spanning Tree Problems under the bottleneck-type Hamming Distance. J. Global Optim. 34, 467–474 (2006)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yang, C., Zhang, J.: Inverse maximum capacity problems. OR Spektrum 20, 97–100 (1998)MATHCrossRefGoogle Scholar
  8. 8.
    Zhang, J., Yang, X., Cai, M.: Some inverse min-max network problems under weighted l 1 and l  ∞  norms. Working Paper. Department of Mathematics, City University of Hong Kong (2004)Google Scholar
  9. 9.
    Zhang, J., Yang, X.: Inverse Maximum Flow Problems Under l  ∞  Norm, l 2 Norm and Hamming Distance. Working Paper. Department of Mathematics, City University of Hong Kong (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiucui Guan
    • 1
  • Jianzhong Zhang
    • 2
  1. 1.Department of MathematicsSoutheast UniversityNanjingP.R. China
  2. 2.Department of System Engineering and Engineering ManagementChinese University of Hong KongHong KongP. R. China

Personalised recommendations