Packing Problems with Orthogonal Rotations

  • Flavio Keidi Miyazawa
  • Yoshiko Wakabayashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


In this extended abstract, we present approximation algorithms for the following packing problems: the strip packing problem, the two-dimensional bin packing problem, the three-dimensional strip packing problem, and the three-dimensional bin packing problem. For all these problems, we consider orthogonal packings where 90° rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 1.613, 2.64, 2.76 and 4.89, respectively. We also present an algorithm for the z-oriented three-dimensional packing problem with asymptotic performance bound 2.64. To our knowledge the bounds presented here are the best known for each problem.


Packing Problem Orthogonal Rotation Asymptotic Performance Strip Packing Problem Orthogonal 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, B.S., Coffman Jr., E.G., Rivest, R.L.: Orthogonal packings in two-dimensions. SIAM Journal on Computing 9, 846–855 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Chung, F.R.K., Garey, M.R., Johnson, D.S.: On packing two-dimensional bins. SIAM Journal on Algebraic and Discrete Methods 3, 66–76 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing - an updated survey. In: Ausiello, G., Lucertini, M., Serafini, P. (eds.) Algorithms design for computer system design, pp. 49–106. Springer, New York (1984)Google Scholar
  4. 4.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing - a survey. In: Hochbaum, D. (ed.) Approximation algorithms. PWS (1997)Google Scholar
  5. 5.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S., Tarjan, R.E.: Performance bounds for level oriented two-dimensional packing algorithms. SIAM J. on Computing 9, 808–826 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fernandez de la Vega, W., Lueker, G.S.: Bin packing can be solved within 1 + ε in linear time. Combinatorica 1(4), 349–355 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass (1973)Google Scholar
  8. 8.
    Kenyon, C., Remila, E.: Approximate strip packing. In: 37th Annual Symposium on Foundations of Computer Science, pp. 31–36 (1996)Google Scholar
  9. 9.
    Li, K., Cheng, K.-H.: Static job scheduling in partitionable mesh connected systems. Journal of Parallel and Distributed Computing 10, 152–159 (1990)CrossRefGoogle Scholar
  10. 10.
    Miyazawa, F.K., Wakabayashi, Y.: An algorithm for the three-dimensional packing problem with asymptotic performance analysis. Algorithmica 18(1), 122–144 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Miyazawa, F.K., Wakabayashi, Y.: Approximation algorithms for the orthogonal z-oriented 3-D packing problem. SIAM Journal on Computing 29(3), 1008–1029 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Flavio Keidi Miyazawa
    • 1
  • Yoshiko Wakabayashi
    • 2
  1. 1.Instituto de ComputaçãoUniversidade Estadual de CampinasCampinasBrazil
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloRua do MatãoBrazil

Personalised recommendations