Skip to main content
SpringerLink
Log in

Le probléme du bin-packing

  • Chapter
Optimisation combinatoire

Part of the book series: Collection IRIS ((IRIS))

Résumé

Supposons que nous ayons n objets, chacun d’une taille donnée, et des boîtes de même capacité. On veut ranger les objets dans les boîtes, en utilisant le moins de boîtes possible. Bien entendu, la taille totale des objets affectés á une boîte ne doit pas dépasser sa capacité.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Références

Littérature générale

  • Coffman, E.G., Garey, M.R., Johnson, D.S. [1996]: Approximation algorithms for binpacking; a survey. In: Approximation Algorithms for NP-Hard Problems (D.S. Hochbaum, ed.), PWS, Boston, 1996

    Google Scholar 

Références citées

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

    Article  MATH  MathSciNet  Google Scholar 

  • Bansal, N., Correa, J.R., Kenyon, C., Sviridenko, M. [2006]: Bin packing in multiple dimensions: inapproximability results and approximation schemes. Mathematics of Operations Research 31 (2006), 31–49

    Article  MATH  MathSciNet  Google Scholar 

  • Caprara, A. [2002]: Packing 2-dimensional bins in harmony. Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (2002), 490–499

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Garey, M.R., Graham, R.L., Johnson, D.S., Yao, A.C. [1976]: Resource constrained scheduling as generalized bin packing. Journal of Combinatorial Theory A 21 (1976), 257–298

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  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., 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., Shmoys, D.B. [1987]: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the ACM 34 (1987), 144–162

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L. [1974]: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3 (1974), 299–325

    Article  MathSciNet  Google Scholar 

  • Karmarkar, N., Karp, R.M. [1982]: An efficient approximation scheme for the onedimensional 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., 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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Plotkin, S.A., Shmoys, D.B., Tardos, É. [1995]: Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research 20 (1995), 257–301

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Yue, M. [1990]: A simple proof of the inequality \( FFD(L) \leqslant \tfrac{{11}} {9}OPT(L) + 1 \), ∀L for the FFD bin-packing algorithm. Report No. 90665, Research Institute for Discrete Mathematics, University of Bonn, 1990

    Google Scholar 

  • Zhang, G. [2005]: A 3-approximation algorithm for two-dimensional bin packing. Operations Research Letters 33 (2005), 121–126

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Discrete Mathematics, University of Bonn, Lennéstraße 2, 53113, Bonn, Germany

    Bernhard Korte & Jens Vygen

  2. Faculté de mathématiques, Université Paris-VI, 175, rue du Chevaleret, 75013, Paris

    Jean Fonlupt (Professeur émérite)

  3. Panthéon-Sorbonne Centre d’économie de la Sorbonne, Université Paris-I, 106-112, boulevard de l’Hôpital, 75013, Paris

    Alexandre Skoda

Authors
  1. Bernhard Korte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Vygen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Fonlupt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexandre Skoda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag France

About this chapter

Cite this chapter

Korte, B., Vygen, J., Fonlupt, J., Skoda, A. (2010). Le probléme du bin-packing. In: Optimisation combinatoire. Collection IRIS. Springer, Paris. https://doi.org/10.1007/978-2-287-99037-3_18

Download citation

  • DOI: https://doi.org/10.1007/978-2-287-99037-3_18

  • Publisher Name: Springer, Paris

  • Print ISBN: 978-2-287-99036-6

  • Online ISBN: 978-2-287-99037-3

Publish with us

Policies and ethics

Search

Navigation