Journal of Parallel and Distributed Computing
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
Approximation algorithms
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
New approximability and inapproximability results for 2-dimensional Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New approximability and inapproximability results for 2-dimensional Bin 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)
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
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 consider a classic multidimensional generalization of the bin packing problem, namely, packing d-dimensional rectangles into the minimum number of unit cubes. Our two results are: an asymptotic polynomial time approximation scheme for packing d-dimensional cubes into the minimum number of unit cubes and a polynomial time algorithm for packing rectangles into at most OPT bins whose sides have length (1 + ε), where OPT denotes the minimum number of unit bins required to pack the rectangles. Both algorithms also achieve the best possible additive constant term. For cubes, this settles the approximability of the problem and represents a significant improvement over the previous best known asymptotic approximation factor of 2 - (2/3)d + ε. For rectangles, this contrasts with the currently best known approximation factor of 1.691....