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

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  • 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
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    References listed on IDEAS

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    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.
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