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Complexity of Partial Inverse Assignment Problem and Partial Inverse Cut Problem

  • Xiaoguang Yang (a1)

Abstract

For a given partial solution, the partial inverse problem is to modify the coefficients such that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum. In this paper, we show that the partial inverse assignment problem and the partial inverse minimum cut problem are NP-hard if there are bound constraints on the changes of coefficients.

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[1] R.K. Ahuja and J.B. Orlin, Inverse optimization, Part I: Linear programming and general problems, Working Paper, SWP#4002. Sloan School of Management, MIT, Cambridge, MA (1998).
[2] R.K. Ahuja and J.B. Orlin, Inverse optimization, Part II: Network flow problems, Working Paper, SWP#4003. Sloan School of Management, MIT, Cambridge, MA (1998).
[3] R.K. Ahuja and J.B. Orlin, Combinatorial algorithms for inverse network flow problems, Working Paper, SWP#4004. Sloan School of Management, MIT, Cambridge, MA (1998).
[4] Cai, M., Yang, X. and Inverse, Y. Li polymatroidal flow problem. J. Comb. Optim. 3 (1999) 115-126.
[5] Cai, M., Yang, X. and Inverse, Y. Li problems of submodular functions on digraphs. J. Optim. Theory Appl. 104 (2000) 559-575.
[6] M. Cai, X. Yang and J. Zhang, Inverse problems with partial given solution, Working Paper. Department of Mathematics, City University of Hong Kong (1997).
[7] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide of the Theory of NP-Completeness. Freeman, San Francisco (1979).
[8] Yang, C. and Zhang, J., Inverse maximum flow and minimum cut problems. Optimization 40 (1997) 147-170.
[9] Zhang, J. and Cai, M., Inverse problem of minimum cuts. ZOR-Math. Methods Oper. Res. 48 (1998) 51-58.
[10] Zhang, J. and Ma, Z., A network flow method for solving some inverse combinatorial optimization problems. Optimization 37 (1996) 59-72.

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