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 journalArticlepeer-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 languageEnglish
Pages (from-to)235-246
Number of pages12
Journal4OR
Volume21
Issue number2
DOIs
StatePublished - Jun 2023

Keywords

  • FPTAS
  • Knapsack problems
  • Parametric optimization
  • Polynomial algorithm

All Science Journal Classification (ASJC) codes

  • Management Information Systems
  • Theoretical Computer Science
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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