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Complexity of determining exact tolerances for min-max combinatorial optimization problems

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  • Ramaswamy, R.
  • Chakravarti, N.
  • Ghosh, D.

    (Groningen University)

Abstract

Suppose that we are given an instance of a combinatorial optimization problemwith min-max objective along with an optimal solution for it. Let the cost of asingle element be varied. We refer to the range of values of the element’s costfor which the given optimal solution remains optimal as its exact tolerance. Inthis paper we examine the problem of determining the exact tolerance of eachelement in combinatorial optimization problems with min-max objectives. Weshow that under very weak assumptions, the exact tolerance of each elementcan be determined in polynomial time if and only if the original optimizationproblem can be solved in polynomial time.

Suggested Citation

  • Ramaswamy, R. & Chakravarti, N. & Ghosh, D., 2000. "Complexity of determining exact tolerances for min-max combinatorial optimization problems," Research Report 00A22, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:00a22
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    File URL: http://irs.ub.rug.nl/ppn/24056653X
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    1. Sotskov, Y. & Sotskova, N. Y. & Werner, F., 1997. "Stability of an optimal schedule in a job shop," Omega, Elsevier, vol. 25(4), pages 397-414, August.
    2. T. Terpstra, 1989. "Asymptotically optimal nonparametric one- and two-way analysis of variance tests for the log linear model under censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 63-90, December.
    3. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    4. A. M. Geoffrion & R. Nauss, 1977. "Exceptional Paper--Parametric and Postoptimality Analysis in Integer Linear Programming," Management Science, INFORMS, vol. 23(5), pages 453-466, January.
    5. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    6. Jenkins, Larry, 1987. "Parametric-objective integer programming using knapsack facets and Gomory cutting planes," European Journal of Operational Research, Elsevier, vol. 31(1), pages 102-109, July.
    7. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
    8. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    9. M. Libura, 1999. "On accuracy of solutions for discrete optimization problems with perturbed coefficientsof the objective function," Annals of Operations Research, Springer, vol. 86(0), pages 53-62, January.
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