Journal of Global Optimization

, Volume 68, Issue 3, pp 601–622 | Cite as

The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems

  • Marcel TurkensteenEmail author
  • Dmitry Malyshev
  • Boris Goldengorin
  • Panos M. Pardalos


The tolerance of an element of a combinatorial optimization problem with respect to its optimal solution is the maximum change of the cost of the element while preserving the optimality of the given optimal solution and keeping all other input data unchanged. Tolerances play an important role in the design of exact and approximation algorithms, but the computation of tolerances requires additional computational time. In this paper, we concentrate on combinatorial optimization problems for which the computation of all tolerances and an optimal solution have almost the same computational complexity as of finding an optimal solution only. We summarize efficient computational methods for computing tolerances for these problems and determine their time complexity experimentally.


Discrete optimization Tolerances Complexity Efficient algorithm 



The research of D.S. Malyshev and P.M. Pardalos is partially supported by LATNA laboratory, National Research University Higher School of Economics. B. Goldengorin’s research is supported by C. Paul Stocker Visiting Professorship provided by the Department of Industrial and Systems Engineering, The Russ College of Engineering, Ohio University, Athens, OH, USA.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Marcel Turkensteen
    • 1
    Email author
  • Dmitry Malyshev
    • 2
  • Boris Goldengorin
    • 3
    • 4
  • Panos M. Pardalos
    • 4
  1. 1.Aarhus UniversityAarhus VDenmark
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussia
  3. 3.Ohio UniversityAthensUSA
  4. 4.University of FloridaGainesvilleUSA

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