A 3-approximation algorithm for two-dimensional bin packing

Operations Research Letters

Volumn 33, Issue 2, 2005, Pages 121-126

  Zhang, Guochuan ^a,b  

^a ZHEJIANG UNIVERSITY   (China)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Absolute worst case ratio; Approximation algorithms; Bin packing

Indexed keywords

APPROXIMATION THEORY; COMPUTER SCIENCE; MATHEMATICAL OPERATORS; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

ABSOLUTE WORST CASE RATIO; APPROXIMATION ALGORITHMS; BIN PACKING; FIRST FIT DECREASING (FFD);

ALGORITHMS;

EID: 9644270632     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2004.04.004     Document Type: Article

References (22)

1. B.S. Baker, E.G. Coffman, R.L. Rivest, Orthogonal packing in two dimensions, SIAM J. Comput. 9 (1980) 846-855.
2. N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2004, pp. 189-196.
3. A. Caprara, Packing 2-dimensional bins in harmony, Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2002, pp. 490-499.
4. A. Caprara, A. Lodi, M. Monaci, An approximation scheme for the two-stage, two-dimensional bin packing problem, Proceedings of the Ninth Conference on Integer Programming and Combinatorial Optimization (IPCO), Lecture Notes in Computer Science, Vol. 2337, Springer, Berlin, 2002, pp. 315-328.
5. F.K.R. Chung, M.R. Gary, D.S. Johnson, On packing two-dimensional bins, SIAM J. Algebraic Discrete Meth. 3 (1982) 66-76.
6. E.G. Coffman Jr., M.R. Garey, D.S. Johnson, Approximation algorithms for bin packing: a survey, in: D. Hochbaum (Ed.), Approximation Algorithms for NP-Hard Problems, PWS Publishing, Boston, 1997, pp. 46-93.
7. J.R. Correa, C. Kenyon, Approximation schemes for multidimensional packing, Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2004, pp. 179-188.
8. W. Fernandez de la Vega, G.S. Luecker, Bin packing can be solved within 1 + ε in linear time, Combinatorica 1 (1981) 349-355.
9. C.E. Ferreira, E.K. Miyazawa, Y. Wakabayashi, Packing squares into squares, Pesqui. Oper. 19 (1999) 223-237.
10. K. Jansen, G. Zhang, On rectangle packing: maximizing benefits, Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2004, pp. 197-206.
11. N. Karmarker, R.M. Karp, An efficient approximation scheme for the one-dimensional bin-packing problem, Proceedings of the 23rd Annual IEEE Symposium on Foundations Computer Science (FOCS), 1982, pp. 312-320.
12. C. Kenyon, E. Remila, A near-optimal solution to a two-dimensional cutting stock problem, Math. Oper. Res. 25 (2000) 645-656.
13. Y. Kohayakawa, F.K. Miyazawa, P. Raghavan, Y. Wakabayashi, Multidimensional cube packing, in: J. Szwarcfiter, S.W. Song (Eds.), Electronic Notes in Discrete Mathematics, Vol. 7, Elsevier, Amsterdam, 2001, 4pp.
14. J.K. Lenstra, D.B. Shmoys, Computing near-optimal schedules, in: P. Chrétienne, et al., (Eds.), Scheduling Theory and Its Application, Wiley, New York, 1995.
15. J.Y.-T. Leung, T.W. Tam, C.S. Wong, G.H. Young, F.Y.L. Chin, Packing squares into a square, J. Parallel Distrib. Comput. 10 (1990) 271-275.
16. A. Lodi, S. Martello, M. Monaci, Two-dimensional bin packing problems: a survey, Eur. J. Oper. Res. 141 (2002) 241-252.
17. A. Lodi, S. Martello, D. Vigo, Recent advance on two-dimensional packing problems, Discrete Appl. Math. 123 (2002) 379-396.
18. I. Schiermeyer, Reverse-fit: a 2-optiraal algorithm for packing rectangles, Proceedings of the 12th Annual European Symposium on Algorithms (ESA), Lecture Notes in Computer Science, Vol. 855, Springer, Berlin, 1994, pp. 290-299.
19. S.S. Seiden, R. van Stee, New bounds for multi-dimensional packing, Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2002, pp. 485-495.
20. D. Simchi-Levi, New worst-case results for the bin packing problem, Nav. Res. Logist. 41 (1994) 579-585.
21. A. Steinberg, A strip-packing algorithm with absolute performance bound 2, SIAM J. Comput. 26 (1997) 401-409.
22. G. Zhang, X. Cai, C.K. Wong, Linear time approximation algorithms for bin packing, Oper. Res. Lett. 26 (2000) 217-222.