On the existence of polynomial-time approximation schemes for the reoptimization of 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:
2011

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Abstract

It is shown that no polynomial-time approximation scheme exists for the reoptimization of the set covering problem in inserting an element into or eliminating it from any set. A similar result is obtained for the minimum graph coloring problem in inserting a vertex with at most two incidence edges and for the minimal bin packing problem in eliminating any element.