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General Knapsack Problems in a Dynamic Setting

Authors Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, Danny Raz

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Author Details

Yaron Fairstein
  • Computer Science Department, Technion, Haifa, Israel
Ariel Kulik
  • Computer Science Department, Technion, Haifa, Israel
Joseph (Seffi) Naor
  • Computer Science Department, Technion, Haifa, Israel
Danny Raz
  • Computer Science Department, Technion, Haifa, Israel

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Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, and Danny Raz. General Knapsack Problems in a Dynamic Setting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.15

Abstract

The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was introduced with this goal in mind. In this model we are given a series of instances of an optimization problem, corresponding to different times, and a solution is provided for each instance. The strive for obtaining near-optimal solutions for each instance on one hand, while maintaining similar solutions for consecutive time units on the other hand, is quantified and integrated into the objective function. In this paper we consider the Generalized Multistage d-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the d-Dimensional Knapsack problem. We present a PTAS for Generalized Multistage d-Knapsack.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Multistage
  • Multiple-Knapsacks
  • Multidimensional Knapsack

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