General approach to estimating the complexity of postoptimality analysis for discrete optimization problems

Authors:
V. A. Mikhailyuk
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2010

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Abstract

It is shown that there does not exist a polynomial algorithm to derive the optimal solution of a set cover problem that differs from the original problem in one position of the constraint matrix if the optimal solution of the original problem is known and P 驴 NP. A similar result holds for the knapsack problem.