A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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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 packing squares with resource augmentation: maximizing the profit
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
An approximation algorithm for sequential rectangle placement
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On the complexity of sequential rectangle placement in IEEE 802.16/WiMAX systems
Information and Computation
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical 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
On the complexity of sequential rectangle placement in IEEE 802.16/WiMAX systems
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A polynomial time approximation scheme for the square packing problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Approximating the orthogonal knapsack problem for hypercubes
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
Theoretical Computer Science
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We consider the problem of packing a set of weighted rectangles into a unit size square frame [0,1] × [0,1] so as to maximize the total weight of the packed rectangles. We present polynomial time approximation schemes (PTASs) that, for any ε0, find (1 - ε)-approximate solutions for two special cases of the problem. In the first case we pack a set of squares whose weights are equal to their areas. In the second case we pack a set of weighted rectangles into an augmented square frame [0,1 + 3ε] × [0,1 + 3ε].