Two Dimensional Packing: The Power of Rotation

  • Leah Epstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


Recently there is a rise in the study of two-dimensional packing problems. In such problems the input items are rectangles which need to be assigned into unit squares. However, most of the previous work concentrated on fixed items. Fixed items have a fixed direction and must be assigned so that their bottom is parallel to the bottom of the bin. In this paper we study two-dimensional bin packing of rotatable items. Those are rectangles which can be rotated by ninety degrees. We give almost tight bounds for bounded space bin packing of rotatable items, and introduce a new unbounded space algorithm. This improves the results of Fujita and Hada.


Competitive Ratio Horizontal Strip Space Algorithm Simple Packing Side Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Coppersmith, D., Raghavan, P.: Multidimensional online bin packing: Algorithms and worst case analysis. Operations Research Letters 8, 17–20 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Csirik, J., van Vliet, A.: An on-line algorithm for multidimensional bin packing. Operations Research Letters 13(3), 149–158 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Csirik, J., Frenk, J.B.G., Labbe, M.: Two dimensional rectangle packing: on line methods and results. Discrete Applied Mathematics 45, 197–204 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dell’Amico, M., Martello, S., Vigo, D.: A lower bound for the non-oriented two-dimensional bin packing problem. Discrete Applied Mathematics 118, 13–24 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Epstein, L., van Stee, R.: Optimal online bounded space multidimensional packing. Technical Report SEN-E0303, CWI, Amsterdam (2003) Google Scholar
  6. 6.
    Fujita, S., Hada, T.: Two-dimensional on-line bin packing problem with rotatable items. Theoretical Computer Science 289(2), 939–952 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Galambos, G., van Vliet, A.: Lower bounds for 1-, 2-, and 3-dimensional online bin packing algorithms. Computing 52, 281–297 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Jensen, T.R., Toft, B.: Graph coloring problems. Wiley, Chichester (1995)zbMATHGoogle Scholar
  9. 9.
    Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis, MIT, Cambridge, MA (1973) Google Scholar
  10. 10.
    Johnson, D.S., et al.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3, 256–278 (1974)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Lee, C.C., Lee, D.T.: A simple online bin packing algorithm. Journal of the ACM 32, 562–572 (1985)zbMATHCrossRefGoogle Scholar
  12. 12.
    Ramanan, P., et al.: Online bin packing in linear time. Journal of Algorithms 10, 305–326 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Seiden, S.S.: On the online bin packing problem. Journal of the ACM 49(5), 640–671 (2002)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Seiden, S.S., van Stee, R.: New bounds for multi-dimensional packing. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 486–495 (2002)Google Scholar
  15. 15.
    van Vliet, A.: An improved lower bound for online bin packing algorithms. Information Processing Letters 43, 277–284 (1992)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Leah Epstein
    • 1
  1. 1.School of Computer ScienceThe Interdisciplinary CenterHerzliyaIsrael

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