Abstract
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.
Research supported in part by the Israel Science Foundation (grant no. 250/01).
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References
Coppersmith, D., Raghavan, P.: Multidimensional online bin packing: Algorithms and worst case analysis. Operations Research Letters 8, 17–20 (1989)
Csirik, J., van Vliet, A.: An on-line algorithm for multidimensional bin packing. Operations Research Letters 13(3), 149–158 (1993)
Csirik, J., Frenk, J.B.G., Labbe, M.: Two dimensional rectangle packing: on line methods and results. Discrete Applied Mathematics 45, 197–204 (1993)
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)
Epstein, L., van Stee, R.: Optimal online bounded space multidimensional packing. Technical Report SEN-E0303, CWI, Amsterdam (2003)
Fujita, S., Hada, T.: Two-dimensional on-line bin packing problem with rotatable items. Theoretical Computer Science 289(2), 939–952 (2002)
Galambos, G., van Vliet, A.: Lower bounds for 1-, 2-, and 3-dimensional online bin packing algorithms. Computing 52, 281–297 (1994)
Jensen, T.R., Toft, B.: Graph coloring problems. Wiley, Chichester (1995)
Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis, MIT, Cambridge, MA (1973)
Johnson, D.S., et al.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3, 256–278 (1974)
Lee, C.C., Lee, D.T.: A simple online bin packing algorithm. Journal of the ACM 32, 562–572 (1985)
Ramanan, P., et al.: Online bin packing in linear time. Journal of Algorithms 10, 305–326 (1989)
Seiden, S.S.: On the online bin packing problem. Journal of the ACM 49(5), 640–671 (2002)
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)
van Vliet, A.: An improved lower bound for online bin packing algorithms. Information Processing Letters 43, 277–284 (1992)
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Epstein, L. (2003). Two Dimensional Packing: The Power of Rotation. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_34
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DOI: https://doi.org/10.1007/978-3-540-45138-9_34
Publisher Name: Springer, Berlin, Heidelberg
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