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A note on online strip packing

Author

Listed:
  • Deshi Ye

    (Zhejiang University)

  • Xin Han

    (University of Hong Kong)

  • Guochuan Zhang

    (Zhejiang University)

Abstract

In online strip packing we are asked to pack a list of rectangles one by one into a vertical strip of unit width, without any information about future rectangles. The goal is to minimize the total height of strip used. The best known algorithm is First Fit Shelf algorithm (Baker and Schwarz in SIAM J. Comput. 12(3):508–525, 1983), which has an absolute competitive ratio of 6.99 under the assumption that the height of each rectangle is bounded from above by one. We improve the shelf algorithm and show an absolute competitive ratio of $7/2+\sqrt{10}\approx 6.6623$ without the restriction on rectangle heights. Our algorithm also beats the best known online algorithm for parallel job scheduling.

Suggested Citation

  • Deshi Ye & Xin Han & Guochuan Zhang, 2009. "A note on online strip packing," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 417-423, May.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:4:d:10.1007_s10878-007-9125-x
    DOI: 10.1007/s10878-007-9125-x
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    Citations

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    Cited by:

    1. Guo, Shouwei & Kang, Liying, 2010. "Online scheduling of malleable parallel jobs with setup times on two identical machines," European Journal of Operational Research, Elsevier, vol. 206(3), pages 555-561, November.
    2. W. Kern & J. J. Paulus, 2013. "A tight analysis of Brown-Baker-Katseff sequences for online strip packing," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 333-344, August.
    3. Yu, Guosong & Mao, Yanling & Xiao, Jiaoliao, 2016. "A new lower bound for online strip packing," European Journal of Operational Research, Elsevier, vol. 250(3), pages 754-759.
    4. Deshi Ye & Danny Z. Chen & Guochuan Zhang, 2018. "Online scheduling of moldable parallel tasks," Journal of Scheduling, Springer, vol. 21(6), pages 647-654, December.
    5. Guosong Yu & Yanling Mao & Jiaoliao Xiao, 2017. "A new upper bound for the online square packing problem in a strip," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1411-1420, May.

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