New classes of fast lower bounds for bin packing problems

Mathematical Programming, Series B

Volumn 91, Issue 1, 2001, Pages 11-31

  Fekete, Sándor P ^a,c   Schepers, Jörg ^b,c  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b IBM   (Germany)

^c UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Bin packing; Dual feasible functions; Lower bounds

Indexed keywords

EID: 0012575285     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100243     Document Type: Article

References (22)

1. Beasley, J.E. (1990): OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069-1072, http://mscmga.ms.ic.ac.uk/info.html
2. Coffmann, Jr., E.G., Garey, M.R., Johnson, D.S. (1997): Approximation algorithms for bin packing: a survey. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-hard Problems. PWS Publishing, Boston, pp. 46-93
3. Chan, L.M.A., Simchi-Levi, D., Bramel, J. (1998): Worst-case analyses, linear programming and the bin-packing problem. Math. Program. 83, 213-227
4. Coffmann, Jr., E.G., Lueker, G.S. (1991): Probabilistic Analysis of Packing and Partitioning Algorithms. Wiley, New York
5. Fekete, S.P., Schepers, J. (1998): New classes of lower bounds for bin packing problems. Proceedings of the 6th International Integer Programming and Combinatorial Optimization Conference. Springer Lecture Notes in Computer Science 1412, 257-270
6. Fekete, S.P., Schepers, J. (1997): A new exact algorithm for general orthogonal d-dimensional knapsack problems. Algorithms - ESA '97, Springer Lecture Notes in Computer Science 1284, 144-156
7. ∼paper
8. ∼paper
9. Fekete, S.P., Schepers, J.: On higher-dimensional packing III: Exact Algorithms. Technical Report 97-290. Available at http://www.zaik.uni-koeln.de/∼paper
10. Fernandez de la Vega, W., Lueker, G.S. (1981): Bin packing can be solved within 1 + ε in linear time. Combinatorica 1, 349-355
11. Garey, M.R., Johnson, D.S. (1979): Computers and Intractability: a guide to the theory of NP-completeness. Freeman, San Francisco
12. Gent, I.P. (1998): Heuristic solution of open bin packing problems. J. Heuristics 3, 299-304
13. Johnson, D.S. (1973): Near-optimal bin packing algorithms. Dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts
14. 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 J. Comput. 3, 299-325
15. Karmarkar, N., Karp, R.M. (1982): An efficient approximation scheme for the one-dimensional bin packing problem. Proc. 23rd Annual Symp. Found. Comp. Sci. (FOCS 1982), pp. 312-320
16. Lueker, G.S. (1983): Bin packing with items uniformly distributed over intervals [a, b]. Proc. 24th Annual Symp. Found. Comp. Sci. (FOCS 1983), pp. 289-297
17. Martello, S., Pisinger, D., Vigo, D. (2000): The three-dimensional bin packing problem. Oper. Res. 48, 256-267
18. Martello, S., Toth, P. (1990): Lower bounds and reduction procedures for the bin packing problem. Discrete Appl. Math. 28, 59-70
19. Martello, S., Toth, P. (1990): Knapsack Problems. Wiley, New York
20. Martello, S, Vigo, D. (1998): Exact solution of the two-dimensional finite bin packing problem. Manage. Sci. 44, 388-399
21. Schepers, J. (1997): Exakte Algorithmen für orthogonale Packungsprobleme. Dissertation, Mathematisches Institut, Universität zu Köln
22. Scholl, A., Klein, R., Jürgens, C. (1997): BISON: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Comput. Oper. Res. 24, 627-645