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Online Minimization Knapsack Problem

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Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

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Abstract

In this paper, we address the online minimization knapsack problem, i. e., the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack. We study the removable model, where it is allowed to remove old items from the knapsack in order to accept a new item. We obtain the following results.

  1. 1

    We propose an 8-competitive deterministic and memoryless algorithm for the problem, which contrasts to the result for the online maximization knapsack problem that no online algorithm has a bounded competitive ratio [8].

  2. 2

    We propose a 2e-competitive randomized algorithm for the problem.

  3. 3

    We derive a lower bound 2 for deterministic algorithms for the problem.

  4. 4

    We propose a 1.618-competitive deterministic algorithm for the case in which each item has its size equal to its cost, and show that this is best possible.

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Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information and Technology, University of Tokyo, Tokyo, 113-8656, Japan

    Xin Han & Kazuhisa Makino

Authors
  1. Xin Han
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  2. Kazuhisa Makino
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Editor information

Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Place des Terasses, Tour Evry 2, 91000, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

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Han, X., Makino, K. (2010). Online Minimization Knapsack Problem. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-12450-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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