Skip to main content

Bin-Packing

  • Chapter
  • First Online:
Combinatorial Optimization

Part of the book series: Algorithms and Combinatorics ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

General Literature

  • 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, 1996

    Google Scholar 

Cited References

  • Baker , B.S. [1985]: A new proof for the First-Fit Decreasing bin-packing algorithm. Journal of Algorithms 6 (1985), 49–70

    Google Scholar 

  • 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), 31–49

    Google Scholar 

  • Bansal , N. and Khan , A. [2014]: Improved approximation algorithm for two-dimensional bin packing. Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (2014), 13–25

    Google Scholar 

  • Caprara , A. [2008]: Packing d-dimensional bins in d stages. Mathematics of Operations Research 33 (2008), 203–215

    Google Scholar 

  • Dósa , G., Li , R., Han , X., and Tuza , Z. [2013]: Tight absolute bound for First Fit Descreasing bin-packing: FFD(L) ≤ 11∕9 OPT(L) + 6∕9. Theoretical Computer Science 510 (2013), 13–61

    Google Scholar 

  • Dósa , G., and Sgall , J. [2013]: First fit bin packing: a tight analysis. Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (2013), 538–549

    Google Scholar 

  • Eisemann , K. [1957]: The trim problem. Management Science 3 (1957), 279–284

    Google Scholar 

  • Eisenbrand , F., and Shmonin , G. [2006]: Carathéodory bounds for integer cones. Operations Research Letters 34 (2006), 564–568

    Google Scholar 

  • Fernandez de la Vega , W., and Lueker , G.S. [1981]: Bin packing can be solved within 1 + ε in linear time. Combinatorica 1 (1981), 349–355

    Google Scholar 

  • 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), 257–298

    Google Scholar 

  • Garey , M.R., and Johnson , D.S. [1975]: Complexity results for multiprocessor scheduling under resource constraints. SIAM Journal on Computing 4 (1975), 397–411

    Google Scholar 

  • Garey , M.R., and Johnson , D.S. [1979]: Computers and Intractability; A Guide to the Theory of NP-Completeness. Freeman, San Francisco 1979, p. 127

    Google Scholar 

  • Gilmore , P.C., and Gomory , R.E. [1961]: A linear programming approach to the cutting-stock problem. Operations Research 9 (1961), 849–859

    Google Scholar 

  • Goemans , M.X., and Rothvoß , T. [2014]: Polynomiality for bin packing with a constant number of item types. Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (2014), 830–839

    Google Scholar 

  • Graham , R.L. [1966]: Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966), 1563–1581

    Google Scholar 

  • 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. 287–326

    Google Scholar 

  • 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), 144–162

    Google Scholar 

  • Hoberg , R., and Rothvoß , T. [2017]: A logarithmic additive integrality gap for bin packing. Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (2017), 2616–2625

    Google Scholar 

  • Horowitz , E., and Sahni , S.K. [1976]: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23 (1976), 317–327

    Google Scholar 

  • 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. 399–410

    Google Scholar 

  • Johnson , D.S. [1973]: Near-Optimal Bin Packing Algorithms. Doctoral Thesis, Dept. of Mathematics, MIT, Cambridge, MA, 1973

    Google Scholar 

  • Johnson , D.S. [1974]: Fast algorithms for bin-packing. Journal of Computer and System Sciences 8 (1974), 272–314

    Google Scholar 

  • Johnson , D.S. [1982]: The NP-completeness column; an ongoing guide. Journal of Algorithms 3 (1982), 288–300, Section 3

    Google Scholar 

  • 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), 299–325

    Google Scholar 

  • 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), 312–320

    Google Scholar 

  • 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 1993

    Google Scholar 

  • Lenstra , H.W. [1983]: Integer Programming with a fixed number of variables. Mathematics of Operations Research 8 (1983), 538–548

    Google Scholar 

  • Papadimitriou , C.H. [1994]: Computational Complexity. Addison-Wesley, Reading 1994, pp. 204–205

    Google Scholar 

  • 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), 257–301

    Google Scholar 

  • Queyranne , M. [1986]: Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems. Operations Research Letters 4 (1986), 231–234

    Google Scholar 

  • Seiden , S.S. [2002]: On the online bin packing problem. Journal of the ACM 49 (2002), 640–671

    Google Scholar 

  • Simchi-Levi , D. [1994]: New worst-case results for the bin-packing problem. Naval Research Logistics 41 (1994), 579–585

    Google Scholar 

  • van Vliet , A. [1992]: An improved lower bound for on-line bin packing algorithms. Information Processing Letters 43 (1992), 277–284

    Google Scholar 

  • Yue , M. [1991]: A simple proof of the inequality \(FFD(L) \leq \frac{11} {9} \mathop{ \mathrm{OPT}}(L) + 1,\forall L\), for the FFD bin-packing algorithm. Acta Mathematicae Applicatae Sinica 7 (1991), 321–331

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Korte, B., Vygen, J. (2018). Bin-Packing. In: Combinatorial Optimization. Algorithms and Combinatorics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-56039-6_18

Download citation

Publish with us

Policies and ethics