Maximum bounded 3-dimensional matching is MAX SNP-complete
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There is no asymptotic PTAS for two-dimensional vector packing
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Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem
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Better approximation algorithms for bin covering
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Mathematics of Operations Research
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FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximating the Advertisement Placement Problem
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Theoretical Computer Science
Approximation schemes for multidimensional 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
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On strip packing With rotations
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An asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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Theoretical Computer Science - Foundations of computation theory (FCT 2003)
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Mathematics of Operations Research
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SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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Bansal and Sviridenko [N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, in: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 189-196] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P=NP. We show that similar approximation hardness results hold for several 2- and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asymptotic approximation ratio of any polynomial time approximation algorithm. Our hardness results apply to the most studied case of 2-dimensional problems with unit square bins, and for 3-dimensional strip packing and covering problems with a strip of unit square base.