Zusammenfassung
Angenommen, wir haben n Objekte verschiedener fester Größen und einige Behälter von gleicher Größe. Unser Problem ist es, die Objekte den Behältern zuzuordnen, mit dem Ziel, die Anzahl der benutzten Behälter zu minimieren. Natürlich darf die Gesamtgröße der einem Behälter zugeordneten Objekte die Größe des Behälters nicht übersteigen.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Literatur
Allgemeine Literatur
Coffman, E.G., Garey, M.R., und Johnson, D.S.: Approximation algorithms for bin-packing; a survey. In: Approximation Algorithms for NP-Hard Problems (D.S. Hochbaum, ed.), PWS, Boston, 1996
Zitierte Literatur
Baker, B.S.: A new proof for the First-Fit Decreasing bin-packing algorithm. Journal of Algorithms 6 (1985), 49–70
Bansal, N., Correa, J.R., Kenyon, C., und Sviridenko, M.: Bin packing in multiple dimensions: inapproximability results and approximation schemes. Mathematics of Operations Research 31 (2006), 31–49
Caprara, A.: Packing d-dimensional bins in d stages. Mathematics of Operations Research 33 (2008), 203–215
Eisemann, K.: The trim problem. Management Science 3 (1957), 279–284
Fernandez de la Vega, W., und Lueker, G.S.: Bin packing can be solved within 1 + in linear time. Combinatorica 1 (1981), 349–355
Garey, M.R., Graham, R.L., Johnson, D.S., und Yao, A.C.: Resource constrained scheduling as generalized bin packing. Journal of Combinatorial Theory A 21 (1976), 257–298
Garey, M.R., und Johnson, D.S.: Complexity results for multiprocessor scheduling under resource constraints. SIAM Journal on Computing 4 (1975), 397–411
Garey, M.R., und Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. Freeman, San Francisco 1979, S. 127
Gilmore, P.C., und Gomory, R.E.: A linear programming approach to the cuttingstock problem. Operations Research 9 (1961), 849–859
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966), 1563–1581
Graham, R.L., Lawler, E.L., Lenstra, J.K., und Rinnooy Kan, A.H.G.: 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, S. 287–326
Hochbaum, D.S., und Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the ACM 34 (1987), 144–162
Horowitz, E., und Sahni, S.K.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23 (1976), 317–327
Johnson, D.S.: Near-Optimal Bin Packing Algorithms. Doctoral Thesis, Dept. of Mathematics, MIT, Cambridge, MA, 1973
Johnson, D.S.: Fast algorithms for bin-packing. Journal of Computer and System Sciences 8 (1974), 272–314
Johnson, D.S.: The NP-completeness column; an ongoing guide. Journal of Algorithms 3 (1982), 288–300, Abschnitt 3
Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., und Graham, R.L.: Worstcase performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3 (1974), 299–325
Karmarkar, N., und Karp, R.M.: 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
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., und Shmoys, D.B.: 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
Lenstra, H.W.: Integer Programming with a fixed number of variables. Mathematics of Operations Research 8 (1983), 538–548
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading 1994, S. 204–205
Plotkin, S.A., Shmoys, D.B., und Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research 20 (1995), 257–301
Queyranne, M.: Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems. Operations Research Letters 4 (1986), 231–234
Seiden, S.S.: On the online bin packing problem. Journal of the ACM 49 (2002), 640–671
Simchi-Levi, D.: New worst-case results for the bin-packing problem. Naval Research Logistics 41 (1994), 579–585
van Vliet, A.: An improved lower bound for on-line bin packing algorithms. Information Processing Letters 43 (1992), 277–284
Yue, M.: A simple proof of the inequality F F D(L) ≤ 11/9 OPT(L) + 1, ∀L for the FFD bin-packing algorithm. Report No. 90665, Research Institute for Discrete Mathematics, University of Bonn, 1990
Zhang, G.: A 3-approximation algorithm for two-dimensional bin packing. Operations Research Letters 33 (2005), 121–126
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Bin-Packing. In: Kombinatorische Optimierung. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76919-4_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-76919-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76918-7
Online ISBN: 978-3-540-76919-4
eBook Packages: Life Science and Basic Disciplines (German Language)