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Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing

Author

Listed:
  • Yong Zhang

    (The University of Hong Kong
    Chinese Academy of Sciences)

  • Francis Y. L. Chin

    (The University of Hong Kong)

  • Hing-Fung Ting

    (The University of Hong Kong)

  • Xin Han

    (Dalian University of Technology)

Abstract

In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P ij . When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90∘-rotation on any plane P ij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For d-dimensional bin packing, an online algorithm with competitive ratio 4 d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing.

Suggested Citation

  • Yong Zhang & Francis Y. L. Chin & Hing-Fung Ting & Xin Han, 2013. "Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 223-236, August.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:2:d:10.1007_s10878-012-9457-z
    DOI: 10.1007/s10878-012-9457-z
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    References listed on IDEAS

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    1. Csirik, J. & Frenk, J.B.G. & Labbé, M., 1993. "Two-dimensional rectangle packing: on-line methods and results," Econometric Institute Research Papers 11700, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

    1. Paulina Grzegorek & Janusz Januszewski, 2019. "Drawer algorithms for 1-space bounded multidimensional hyperbox packing," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 1011-1044, April.
    2. Feifeng Zheng & Li Luo & E. Zhang, 2015. "NF-based algorithms for online bin packing with buffer and bounded item size," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 360-369, August.
    3. Jing Chen & Xin Han & Kazuo Iwama & Hing-Fung Ting, 2015. "Online bin packing with (1,1) and (2, $$R$$ R ) bins," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 276-298, August.

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