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Bin-Packing

  • Bernhard Korte
  • Jens Vygen
Chapter
Part of the Algorithms and Combinatorics book series (AC, volume 21)

Abstract

Suppose we have n objects, each of a given size, and some bins of equal capacity. We want to assign the objects to the bins, using as few bins as possible. Of course the total size of the objects assigned to one bin should not exceed its capacity.

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References

  1. Coffman, E.G., Garey, M.R., and Johnson, D.S. [1996]: Approximation algorithms for bin-packing; a survey. In: Approximation Algorithms for NP-Hard Problems (D.S. Hochbaum, ed.), PWS, Boston, 1996Google Scholar
  2. Baker, B.S. [1985]: A new proof for the First-Fit Decreasing bin-packing algorithm. Journal of Algorithms 6 (1985), 49–70CrossRefMATHMathSciNetGoogle Scholar
  3. Bansal, N., Correa, J.R., Kenyon, C., and Sviridenko, M. [2006]: Bin packing in multiple dimensions: inapproximability results and approximation schemes. Mathematics of Operations Research 31 (2006), 31–49CrossRefMATHMathSciNetGoogle Scholar
  4. Caprara, A. [2008]: Packing d-dimensional bins in d stages. Mathematics of Operations Research 33 (2008), 203–215CrossRefMATHMathSciNetGoogle Scholar
  5. Dósa, G. [2007]: The tight bound of first fit decreasing bin-packing algorithm is FFD(I) ≤ 11 ∕ 9OPT(I) + 6 ∕ 9. In: Combinatorics, Algorithms, Probabilistic and Experimental Methodologies; LNCS 4614 (Chen, B., Paterson, M., Zhang, G., eds.), Springer, Berlin 2007, pp. 1–11Google Scholar
  6. Eisemann, K. [1957]: The trim problem. Management Science 3 (1957), 279–284CrossRefMATHMathSciNetGoogle Scholar
  7. Fernandez de la Vega, W., and Lueker, G.S. [1981]: Bin packing can be solved within 1 + ε in linear time. Combinatorica 1 (1981), 349–355CrossRefMATHMathSciNetGoogle Scholar
  8. Garey, M.R., Graham, R.L., Johnson, D.S., and Yao, A.C. [1976]: Resource constrained scheduling as generalized bin packing. Journal of Combinatorial Theory A 21 (1976), 257–298CrossRefMATHMathSciNetGoogle Scholar
  9. Garey, M.R., and Johnson, D.S. [1975]: Complexity results for multiprocessor scheduling under resource constraints. SIAM Journal on Computing 4 (1975), 397–411CrossRefMATHMathSciNetGoogle Scholar
  10. Garey, M.R., and Johnson, D.S. [1979]: Computers and Intractability; A Guide to the Theory of NP-Completeness. Freeman, San Francisco 1979, p. 127Google Scholar
  11. Gilmore, P.C., and Gomory, R.E. [1961]: A linear programming approach to the cutting-stock problem. Operations Research 9 (1961), 849–859CrossRefMATHMathSciNetGoogle Scholar
  12. Graham, R.L. [1966]: Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966), 1563–1581Google Scholar
  13. Graham, R.L., Lawler, E.L., Lenstra, J.K., and Rinnooy Kan, A.H.G. [1979]: Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Discrete Optimization II; Annals of Discrete Mathematics 5 (P.L. Hammer, E.L. Johnson, B.H. Korte, eds.), North-Holland, Amsterdam 1979, pp. 287–326Google Scholar
  14. Hochbaum, D.S., and Shmoys, D.B. [1987]: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the ACM 34 (1987), 144–162CrossRefMathSciNetGoogle Scholar
  15. Horowitz, E., and Sahni, S.K. [1976]: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23 (1976), 317–327CrossRefMATHMathSciNetGoogle Scholar
  16. Jansen, K., Prädel, L., and Schwarz, U.M. [2009]: Two for one: tight approximation of 2D bin packing. In: Algorithms and Data Structures – Proceedings of the 11th Algorithms and Data Structures Symposium; LNCS 5664 (F. Dehne, M. Gavrilova, J.-R. Sack, C.D. Tóth, eds.), Springer, Berlin 2009, pp. 399–410Google Scholar
  17. Johnson, D.S. [1973]: Near-Optimal Bin Packing Algorithms. Doctoral Thesis, Dept. of Mathematics, MIT, Cambridge, MA, 1973Google Scholar
  18. Johnson, D.S. [1974]: Fast algorithms for bin-packing. Journal of Computer and System Sciences 8 (1974), 272–314CrossRefMATHMathSciNetGoogle Scholar
  19. Johnson, D.S. [1982]: The NP-completeness column; an ongoing guide. Journal of Algorithms 3 (1982), 288–300, Section 3Google Scholar
  20. Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., and Graham, R.L. [1974]: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3 (1974), 299–325CrossRefMathSciNetGoogle Scholar
  21. Karmarkar, N., and Karp, R.M. [1982]: An efficient approximation scheme for the one-dimensional bin-packing problem. Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science (1982), 312–320Google Scholar
  22. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., and Shmoys, D.B. [1993]: Sequencing and scheduling: algorithms and complexity. In: Handbooks in Operations Research and Management Science; Vol. 4 (S.C. Graves, A.H.G. Rinnooy Kan, P.H. Zipkin, eds.), Elsevier, Amsterdam 1993Google Scholar
  23. Lenstra, H.W. [1983]: Integer Programming with a fixed number of variables. Mathematics of Operations Research 8 (1983), 538–548CrossRefMATHMathSciNetGoogle Scholar
  24. Papadimitriou, C.H. [1994]: Computational Complexity. Addison-Wesley, Reading 1994, pp. 204–205Google Scholar
  25. Plotkin, S.A., Shmoys, D.B., and Tardos, É. [1995]: Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research 20 (1995), 257–301CrossRefMATHMathSciNetGoogle Scholar
  26. Queyranne, M. [1986]: Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems. Operations Research Letters 4 (1986), 231–234CrossRefMATHMathSciNetGoogle Scholar
  27. Seiden, S.S. [2002]: On the online bin packing problem. Journal of the ACM 49 (2002), 640–671CrossRefMathSciNetGoogle Scholar
  28. Simchi-Levi, D. [1994]: New worst-case results for the bin-packing problem. Naval Research Logistics 41 (1994), 579–585CrossRefMATHMathSciNetGoogle Scholar
  29. van Vliet, A. [1992]: An improved lower bound for on-line bin packing algorithms. Information Processing Letters 43 (1992), 277–284CrossRefMATHMathSciNetGoogle Scholar
  30. Xia, B., and Tan, Z. [2010]: Tighter bounds of the First Fit algorithm for the bin-packing problem. Discrete Applied Mathematics 158 (2010), 1668–1675CrossRefMATHMathSciNetGoogle Scholar
  31. Yue, M. [1991]: A simple proof of the inequality FFD(L) ≤ \frac{11} {9} OPT (L) + 1,  ∀L, for the FFD bin-packing algorithm. Acta Mathematicae Applicatae Sinica 7 (1991), 321–331CrossRefMATHGoogle Scholar
  32. Zhang, G. [2005]: A 3-approximation algorithm for two-dimensional bin packing. Operations Research Letters 33 (2005), 121–126CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Research Institute for Discrete MathematicsUniversity of BonnBonnGermany

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