Journal of Parallel and Distributed Computing
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
The hardness of approximation: gap location
Computational Complexity
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
On multi-dimensional packing problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation schemes for multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal online bounded space multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation schemes for multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal online bounded space multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On packing squares with resource augmentation: maximizing the profit
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
An asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM Transactions on Algorithms (TALG)
Three-dimensional packings with rotations
Computers and Operations Research
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Two for One: Tight Approximation of 2D Bin Packing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
On efficient weighted rectangle packing with large resources
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Inapproximability results for orthogonal rectangle packing problems with rotations
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Resource augmentation in two-dimensional packing with orthogonal rotations
Operations Research Letters
A 3-approximation algorithm for two-dimensional bin packing
Operations Research Letters
An approximation algorithm for square packing
Operations Research Letters
SIAM Journal on Discrete Mathematics
Multi-dimensional packing with conflicts
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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We study the 2-dimensional generalization of the classical Bin Packing problem: Given a collection of rectangles of specified size (width, height), the goal is to pack these into minimum number of square bins of unit size. A long history of results exists for this problem and its special cases [3, 14, 10, 18, 9, 1, 15]. Currently, the best known approximation algorithm achieves a guarantee of 1.69 in the asymptotic case (i.e. when the optimum uses a large number of bins) [1]. However, an important open question has been whether 2-dimensional bin packing is essentially similar to the 1-dimensional case in that it admits an asymptotic polynomial time approximation scheme (APTAS) [8, 13] or not? We answer the question in the negative and show that the problem is APX hard in the asymptotic case. On the other hand, we give an asymptotic PTAS for the special case when all the rectangles to be packed are squares (or more generally hypercubes). This improves upon the previous best known guarantee of 1.454 for d = 2 [9] and 2 - (2/3)d for d 2 [15], and settles the approximability for this special case.