The Maximum Resource Bin Packing Problem

  • Joan Boyar
  • Leah Epstein
  • Lene M. Favrholdt
  • Jens S. Kohrt
  • Kim S. Larsen
  • Morten Monrad Pedersen
  • Sanne Wøhlk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3623)


Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems.

For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing.

For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms.

We study the general versions of the problems as well as the parameterized versions where there is an upper bound of \(\frac{1}{k}\) on the item sizes, for some integer k.


Approximation Ratio Competitive Ratio Small Item Item Size Travel Salesperson Problem 
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.
    Arkin, E.M., Bender, M.A., Mitchell, J.S.B., Skiena, S.: The Lazy Bureaucrat scheduling problem. Information and Computation 184(1), 129–146 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Assman, S.F., Johnson, D.S., Kleitman, D.J., Leung, J.Y.-T.: On a dual version of the onedimensional bin packing problem. J. Alg. 5(4), 502–525 (1984)CrossRefGoogle Scholar
  3. 3.
    Bar-Noy, A., Ladner, R.E., Tamir, T.: Windows scheduling as a restricted version of bin packing. In: Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 224–233. ACM, New York (2004)Google Scholar
  4. 4.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  5. 5.
    Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. In: CIAC 2003. LNCS, vol. 2653, pp. 58–69. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line bin packing algorithms. Technical report PP–2003–13, Department of Mathematics and Computer Science, University of Southern Denmark (2003)Google Scholar
  7. 7.
    Csirik, J., Frenk, J.B.G., Labbé, M., Zhang, S.: Two simple algorithms for bin covering. Acta Cybernetica 14(1), 13–25 (1999)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Csirik, J., Johnson, D.S., Kenyon, C.: Better approximation algorithms for bin covering. In: Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 557–566 (2001)Google Scholar
  9. 9.
    Epstein, L., Levy, M.: Online interval coloring and variants. In: Proc. 32nd International Colloquium on Automata, Languages and Programming (2005) (to appear)Google Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability – A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  11. 11.
    Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45, 1563–1581 (1966)Google Scholar
  12. 12.
    Hassin, R., Rubinstein, S.: An approximation algorithm for the maximum traveling salesman problem. Information Processing Letters 67(3), 125–130 (1998)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Hochbaum, D.S. (ed.): Approximation Algorithms for NP-Hard Problems. PWS Publishing Company (1997)Google Scholar
  14. 14.
    Jansen, K., Solis-Oba, R.: An asymptotic fully polynomial time approximation scheme for bin covering. Theoretical Computer Science 306(1–3), 543–551 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comp. 3, 299–325 (1974)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Karger, D.R., Motwani, R., Ramkumar, G.D.S.: On approximating the longest path in a graph. Algorithmica 18(1), 82–98 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joan Boyar
    • 1
  • Leah Epstein
    • 2
  • Lene M. Favrholdt
    • 1
  • Jens S. Kohrt
    • 1
  • Kim S. Larsen
    • 1
  • Morten Monrad Pedersen
    • 1
  • Sanne Wøhlk
    • 3
  1. 1.Dept. of Math. and Computer ScienceUniversity of SouthernDenmark
  2. 2.Dept. of MathematicsUniversity of HaifaIsrael
  3. 3.Dept. of Organization and ManagementUniversity of SouthernDenmark

Personalised recommendations