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On-Line Algorithms for Cardinality Constrained Bin Packing Problems

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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Abstract

The bin packing problem asks for a packing of a list of items from [0, 1] into the smallest possible number of bins having unit capacity. The k-item bin packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two efficient approximation algorithms for the on-line version of this problem. We show that, for increasing values of k, the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has an asymptotic worst-case performance ratio of 2. Both heuristics considerably improve upon the best known result 2.7 of Krause, Shen and Schwetman. Moreover, we present algorithms for k = 2 and k = 3, where the result for k = 2 is best possible.

Supported by the Deutsche Forschungsgemeinschaft

Supported by the ESRC Management Research Fellowship.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität München, D-80290, München, Germany

    Luitpold Babel

  2. Warwick Business School, University of Warwick, CV4 7AL, Coventry, UK

    Bo Chen

  3. Institut für Statistik und Operations Research, Universität Graz Universitätsstraße 15, A-8010, Graz, Austria

    Hans Kellerer

  4. Faculty of Applied Mathematics and Computer Science, University of Minsk, 220080, Minsk, Belarus

    Vladimir Kotov

Authors
  1. Luitpold Babel
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  2. Bo Chen
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  3. Hans Kellerer
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  4. Vladimir Kotov
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Babel, L., Chen, B., Kellerer, H., Kotov, V. (2001). On-Line Algorithms for Cardinality Constrained Bin Packing Problems. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_59

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  • DOI: https://doi.org/10.1007/3-540-45678-3_59

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

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