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Knapsack problem with objective value gaps

Abstract : We study a 0-1 knapsack problem, in which the objective value is forbidden to take some values. We call gaps related forbidden intervals. The problem is NP-hard and pseudo-polynomially solvable independently on the measure of gaps. If the gaps are large, then the problem is polynomially non-approximable. A non-trivial special case with respect to the approximate solution appears when the gaps are small and polynomially close to zero. For this case, two fully polynomial time approximation schemes are proposed. The results can be extended for the constrained longest path problem and other combinatorial problems.
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Submitted on : Friday, May 13, 2016 - 11:27:21 AM
Last modification on : Wednesday, June 24, 2020 - 4:19:36 PM
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Alexandre Dolgui, Mikhail Y. Kovalyov, Alain Quilliot. Knapsack problem with objective value gaps. Optimization Letters, Springer Verlag, 2017, 11 (1), pp.31-39. ⟨10.1007/s11590-016-1043-3⟩. ⟨hal-01315452⟩

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