Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
SIAM Journal on Discrete Mathematics
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
A Tale of Two Dimensional Bin Packing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
A Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A polynomial time approximation scheme for the square packing problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
SIAM Journal on Discrete Mathematics
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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The two-dimensional bin packing problem is a generalization of the classical bin packing problem and is defined as follows. Given a collection of rectangles specified by their width and height, pack these into a minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions require a large number of bins [N. Bansal, J. Correa, C. Kenyon, M. Sviridenko, Bin packing in multiple dimensions: Inapproximability results and approximation schemes, Math. Oper. Res. 31 (1) (2006) 31-49]. On the positive side, there exists a polynomial time algorithm that uses OPT bins whose sides have length (1+@e), where OPT denotes the number of unit sized bins used by the optimum solution [N. Bansal, J. Correa, C. Kenyon, M. Sviridenko, Bin packing in multiple dimensions: Inapproximability results and approximation schemes, Math. Oper. Res. 31 (1) (2006) 31-49]. A natural question that remains is the approximability of the problem when we are allowed to relax the size of the unit bins in only one dimension. In this paper, we show that there exists an asymptotic polynomial time approximation scheme for packing rectangles into bins of size 1x(1+@e).