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International Workshop on Approximation Algorithms for Combinatorial Optimization

International Workshop on Randomization and Approximation Techniques in Computer Science

APPROX 2007, RANDOM 2007: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques pp 180–188Cite as

Optimal Resource Augmentations for Online Knapsack

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4627))

Abstract

It is known that online knapsack is not competitive. This negative result remains true even if the items are removable. In this paper we consider online removable knapsack with resource augmentation, in which we hold a knapsack of capacity R ≥ 1.0 and aim at maintaining a feasible packing to maximize the total weight of the items packed. Accepted items can be removed to leave room for newly arriving items. Once an item is rejected/removed it can not be considered again. We evaluate an online algorithm by comparing the resulting packing to an optimal packing that uses a knapsack of capacity one. Optimal online algorithms are derived for both the weighted case (items have arbitrary weights) and the un-weighted case (the weight of an item is equal to its size).

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Author information

Authors and Affiliations

  1. School of Informatics, Kyoto University, Japan

    Kazuo Iwama

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Guochuan Zhang

Authors
  1. Kazuo Iwama
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  2. Guochuan Zhang
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Editor information

Editors and Affiliations

  1. Computer Science Dept., Princeton University, 35 Olden Street, NJ 08540-5233, Princeton, USA

    Moses Charikar

  2. Institut für Informatik, Christian-Albrechts-Universität zu Kiel,, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Omer Reingold

  4. Centre Universitaire d’Informatique,, Battelle bâtiment A, route de Drize 7, 1227, Geneva, Carouge, Switzerland

    José D. P. Rolim

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© 2007 Springer-Verlag Berlin Heidelberg

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Iwama, K., Zhang, G. (2007). Optimal Resource Augmentations for Online Knapsack. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_13

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  • DOI: https://doi.org/10.1007/978-3-540-74208-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74207-4

  • Online ISBN: 978-3-540-74208-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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