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Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal

Authors Matthias Gehnen , Moritz Stocker

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LIPIcs.STACS.2026.43.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Adversary models
Keywords
  • online problems
  • online knapsack
  • unbounded knapsack
  • removal

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Abstract

We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a knapsack with a fixed weight limit. An item may be packed an arbitrary number of times and items may be removed from the knapsack at any time without cost. The goal is to maximize the total value of items packed, while respecting a weight limit. We show that this is one of the very few natural online knapsack variants that allow for competitive deterministic algorithms in the general setting, by providing an algorithm with competitivity 1.6911. We complement this with a lower bound of 1.5877. 
We also analyze the proportional setting, where the weight and value of any single item agree, and show that deterministic algorithms can be exactly 3/2-competitive. Lastly, we give lower and upper bounds of 6/5 and 4/3 on the competitivity of randomized algorithms in this setting.

Cite As Get BibTex

Matthias Gehnen and Moritz Stocker. Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.43

Author Details

Matthias Gehnen
  • Department of Computer Science, RWTH Aachen University, Germany
Moritz Stocker
  • Department of Computer Science, ETH Zurich, Switzerland

References

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