Max–max, max–min, min–max and min–min knapsack problems with a parametric constraint

Nir Halman; Mikhail Y. Kovalyov; Alain Quilliot

doi:10.1007/s10288-022-00509-1

Max–max, max–min, min–max and min–min knapsack problems with a parametric constraint

Nir Halman, Mikhail Y. Kovalyov, Alain Quilliot

Research output: Contribution to journal › Article › peer-review

Abstract

Max–max, max–min, min–max and min–min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the parameter. Algorithms with O(nlog n) and O(n²) running times are proposed for the problems with a fixed parameter and for the general problem, respectively, where n is the number of items to be packed into the knapsack. The latter algorithm determines optimal solution values for all values of the parameter in O(nlog ²n) time. The problem of deciding whether there exists a single optimal solution for all values of the numerical parameter is proved to be NP-complete.

Original language	English
Pages (from-to)	235-246
Number of pages	12
Journal	4OR
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s10288-022-00509-1
State	Published - Jun 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

Nir Halman is supported in part by the Israel Science Foundation grants 399/17 and 1074/21, and by the United States-Israel Binational Science Foundation (BSF). Mikhail Y. Kovalyov and Alain Quilliot are supported in part by French ANR, Labex IMOBS3, and PGMO Program.

Funders	Funder number
Labex IMOBS3
United States - Israel Binational Science Foundation
Agence Nationale de la Recherche
United States-Israel Binational Science Foundation
Israel Science Foundation	399/17, 1074/21

Keywords

FPTAS
Knapsack problems
Parametric optimization
Polynomial algorithm

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10.1007/s10288-022-00509-1

Cite this

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Max–max, max–min, min–max and min–min knapsack problems with a parametric constraint

Abstract

Bibliographical note

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Keywords

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