Integer knapsack problems with profit functions of the same value range

Evgeny Gurevsky (), Dmitry Kopelevich, Sergey Kovalev and Mikhail Y. Kovalyov
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Evgeny Gurevsky: LS2N, Université de Nantes
Dmitry Kopelevich: Belarusian State University
Sergey Kovalev: INSEEC Business School
Mikhail Y. Kovalyov: United Institute of Informatics Problems, NASB

4OR, 2023, vol. 21, issue 3, No 2, 405-419

Abstract: Abstract Integer knapsack problems with profit functions of the same value range are studied. Linear time algorithms are presented for the case of convex non-decreasing profit functions, and an NP-hardness proof and a fully polynomial-time approximation scheme are provided for the case of arbitrary non-negative non-decreasing profit functions. Fast solution procedures are also devised for the bottleneck counterparts of these problems. Computational complexity of the case with concave profit functions remains open.

Keywords: Knapsack problem; Convex optimization; Median finding; NP-hardness; FPTAS; 90C27; 90C39 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10288-022-00514-4

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