Journal of Parallel and Distributed Computing
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
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 rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Advertisement Placement Problem
Journal of Scheduling
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
An asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
Approximation algorithms for 3D orthogonal Knapsack
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of 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
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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Given a list of d-dimensional cuboid items with associated profits, the orthogonal knapsack problem asks for a packing of a selection with maximal profit into the unit cube. We restrict the items to hypercube shapes and derive a $(\frac{5}{4}+\epsilon)$-approximation for the two-dimensional case. In a second step we generalize our result to a $(\frac{2^d+1}{2^d}+\epsilon)$-approximation for d-dimensional packing.