Knapsack problem with objective value gaps

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• 作者：Alexander Dolgui ; Mikhail Y. Kovalyov ; Alain Quilliot
• 关键词：Knapsack problem ; Computational complexity ; Fully polynomial time approximation scheme ; Forbidden values
• 刊名：Optimization Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：31-39
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Optimization; Operation Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation;
• 出版者：Springer Berlin Heidelberg
• ISSN：1862-4480
• 卷排序：11

文摘

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.