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Online Removable Square Packing

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Abstract

The online removable square packing problem is a two-dimen-sional version of the online removable Knapsack problem. For a sequence of squares with side length at most 1, we are requested to pack a subset of them into a unit square bin in an online fashion where the online player can decide whether to take the current square or not and which squares currently in the unit square to remove. The goal is to maximize the total packed area. Our results include: (i) No online algorithm can achieve a better competitive ratio than \((\sqrt{5}+3)/2\approx 2.618\) . (ii) The matching upper bound is achieved by a relatively simple online algorithm if repacking is allowed. (iii) Without repacking, we can achieve an upper bound of 3 by using the concept of bricks of Januszewski and Lassak. (iv) The offline version of the problem admits a PTAS.

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Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Xin Han & Kazuo Iwama

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

    Guochuan Zhang

Authors
  1. Xin Han
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  2. Kazuo Iwama
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  3. Guochuan Zhang
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Corresponding author

Correspondence to Xin Han.

Additional information

Research supported by NSFC (10231060).

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Han, X., Iwama, K. & Zhang, G. Online Removable Square Packing. Theory Comput Syst 43, 38–55 (2008). https://doi.org/10.1007/s00224-007-9039-0

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  • DOI: https://doi.org/10.1007/s00224-007-9039-0

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