IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v9y2005i1d10.1007_s10878-005-5481-6.html
   My bibliography  Save this article

Average-Case Performance Analysis of a 2D Strip Packing Algorithm—NFDH

Author

Listed:
  • Xiaodong Gu

    (University of Science and Technology of China)

  • Guoliang Chen

    (University of Science and Technology of China)

  • Yinlong Xu

    (University of Science and Technology of China)

Abstract

The two-dimensional strip packing problem is a generalization of the classic one-dimensional bin packing problem. It has many important applications such as costume clipping, material cutting, real-world planning, packing, scheduling etc. Average-case performance analysis of approximation algorithms attracts a lot of attention because it plays a crucial role in selecting an appropriate algorithm for a given application. While approximation algorithms for two-dimensional packing are frequently presented, the results of their average-case performance analyses have seldom been reported due to intractability. In this paper, we analyze the average-case performance of Next Fit Decreasing Height (NFDH) algorithm, one of the first strip packing algorithms proposed by Coffman, Jr. in 1980. We prove that the expected height of packing with NFDH algorithm, when the heights and widths of the rectangle items are independent and both obey (0, 1] uniform distribution, is about n/3, where n is the number of rectangle items. We also validate the theoretical result with experiments.

Suggested Citation

  • Xiaodong Gu & Guoliang Chen & Yinlong Xu, 2005. "Average-Case Performance Analysis of a 2D Strip Packing Algorithm—NFDH," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 19-34, February.
    • Handle: RePEc:spr:jcomop:v:9:y:2005:i:1:d:10.1007_s10878-005-5481-6
    DOI: 10.1007/s10878-005-5481-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-005-5481-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-005-5481-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Coffman, E. G. & Shor, P. W., 1990. "Average-case analysis of cutting and packing in two dimensions," European Journal of Operational Research, Elsevier, vol. 44(2), pages 134-144, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
    2. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    3. Gardeyn, Jeroen & Wauters, Tony, 2022. "A goal-driven ruin and recreate heuristic for the 2D variable-sized bin packing problem with guillotine constraints," European Journal of Operational Research, Elsevier, vol. 301(2), pages 432-444.
    4. Hong, Shaohui & Zhang, Defu & Lau, Hoong Chuin & Zeng, XiangXiang & Si, Yain-Whar, 2014. "A hybrid heuristic algorithm for the 2D variable-sized bin packing problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 95-103.
    5. Yi-Ping Cui & Yongwu Zhou & Yaodong Cui, 2017. "Triple-solution approach for the strip packing problem with two-staged patterns," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 588-604, August.
    6. Kurt R. Heidelberg & Gregory S. Parnell & James E. Ames, 1998. "Automated air load planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 751-768, December.
    7. Hadjiconstantinou, Eleni & Christofides, Nicos, 1995. "An exact algorithm for general, orthogonal, two-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 83(1), pages 39-56, May.
    8. Ortmann, Frank G. & Ntene, Nthabiseng & van Vuuren, Jan H., 2010. "New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems," European Journal of Operational Research, Elsevier, vol. 203(2), pages 306-315, June.
    9. Bortfeldt, Andreas, 2006. "A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces," European Journal of Operational Research, Elsevier, vol. 172(3), pages 814-837, August.
    10. Baldacci, Roberto & Boschetti, Marco A., 2007. "A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1136-1149, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:9:y:2005:i:1:d:10.1007_s10878-005-5481-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.