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An Optimal Algorithm for Online Multiple Knapsack

Authors Marcin Bienkowski , Maciej Pacut , Krzysztof Piecuch

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Author Details

Marcin Bienkowski
  • Institute of Computer Science, University of Wrocław, Poland
Maciej Pacut
  • Faculty of Computer Science, University of Vienna, Austria
Krzysztof Piecuch
  • Institute of Computer Science, University of Wrocław, Poland

Funding

Research supported by Polish National Science Centre grants 2016/22/E/ST6/00499 and 2016/23/N/ST6/03412.

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Marcin Bienkowski, Maciej Pacut, and Krzysztof Piecuch. An Optimal Algorithm for Online Multiple Knapsack. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.13

Abstract

In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of n bins (knapsacks) of equal size. The gain of an algorithm is equal to the sum of sizes of accepted items and the goal is to maximize the total gain.
So far, for this natural problem, the best solution was the 0.5-competitive algorithm FirstFit (the result holds for any n ≥ 2). We present the first algorithm that beats this ratio, achieving the competitive ratio of 1/(1+ln(2))-O(1/n) ≈ 0.5906 - O(1/n). Our algorithm is deterministic and optimal up to lower-order terms, as the upper bound of 1/(1+ln(2)) for randomized solutions was given previously by Cygan et al. [TOCS 2016].

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online knapsack
  • multiple knapsacks
  • bin packing
  • competitive analysis

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References

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