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Improved Lower Bound for Online Strip Packing

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We study the online strip packing problem and derive an improved lower bound of ρ≥2.589… for the competitive ratio of this problem. The construction is based on modified “Brown-Baker-Katseff sequences” (Brown et al. in Acta Inform. 18:207–225, 1982) using only two types of rectangles. In addition, we present an online algorithm with competitive ratio \((3+\sqrt{5})/2 = 2.618\ldots\) for packing instances of this type.

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References

  1. Brown, D.J., Baker, B.S., Katseff, H.P.: Lower bounds for online two-dimensional packing algorithms. Acta Inform. 18, 207–225 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baker, B.S., Coffman, E.G., Rivest, R.L.: Orthogonal packings in two dimensions. SIAM J. Comput. 9(4), 846–855 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kenyon, C., Remila, E.: Approximate strip packing. In: Proc. of 37th FOCS, pp. 31–36 (1996)

    Google Scholar 

  4. Ye, D., Han, X., Zhang, G.: A note on online strip packing. J. Comb. Optim. 17(4), 417–423 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hurink, J., Paulus, J.: Online algorithm for parallel job scheduling and strip packing. In: WAOA: Proc. of 5th Workshop on Approximation and Online Algorithms, pp. 67–74 (2007)

    Google Scholar 

  6. Baker, B.S., Schwarz, J.S.: Shelf algorithms for two-dimensional packing problems. SIAM J. Comput. 12(3), 508–525 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  7. Csirik, J., Woeginger, G.J.: Shelf algorithm for online strip packing. Inf. Process. Lett. 63, 171–175 (1997)

    Article  MathSciNet  Google Scholar 

  8. Han, X., Iwama, K., Ye, D., Zhang, G.: Strip packing vs. bin packing. In: Proc. 3rd International Conference on Algorithmic Aspects in Information and Management (AAIM). Lecture Notes in Computer Science, vol. 4508, pp. 358–367. Springer, Berlin (2007)

    Chapter  Google Scholar 

  9. Johannes, B.: Scheduling parallel jobs to minimize the makespan. J. Sched. 9(5), 433–452 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hurink, J., Paulus, J.: Online scheduling of parallel jobs on two machines is 2-competitive. Oper. Res. Lett. 36(1), 51–56 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kern, W., Paulus, J.: A tight analysis of Brown-Baker-Katseff sequences for online strip packing. J. Comb. Optim. (2012). doi:10.1007/s10878-012-9463-1

    Google Scholar 

  12. Harren, R., Kern, W.: Improved lower bound for online strip packing. In: WAOA 2011 Proceedings (2011)

    Google Scholar 

  13. Fuchs, B., Hochstaettler, W., Kern, W.: Online matching on a line. Theor. Comput. Sci. 332(1–3), 251–264 (2005)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik (MPII), Campus E1 4, 66123, Saarbrücken, Germany

    Rolf Harren

  2. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500, AE Enschede, The Netherlands

    Walter Kern

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  1. Rolf Harren
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  2. Walter Kern
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Correspondence to Walter Kern.

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Harren, R., Kern, W. Improved Lower Bound for Online Strip Packing. Theory Comput Syst 56, 41–72 (2015). https://doi.org/10.1007/s00224-013-9494-8

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