Journal of Parallel and Distributed Computing
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
Mathematics of Operations Research
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximating the Advertisement Placement Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
A New Fully Polynomial Approximation Scheme for the Knapsack Problem
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
New approximability and inapproximability results for 2-dimensional Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Chips on wafers, or packing rectangles into grids
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
On packing squares with resource augmentation: maximizing the profit
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On-line scheduling mesh jobs with dependencies
Theoretical Computer Science
Maximizing the throughput of parallel jobs on hypercubes
Information Processing Letters
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Spectrum Bidding in Wireless Networks and Related
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
An approximation algorithm for sequential rectangle placement
Information Processing Letters
On the complexity of sequential rectangle placement in IEEE 802.16/WiMAX systems
Information and Computation
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Mathematics of Operations Research
ACM Transactions on Computer-Human Interaction (TOCHI)
Two for One: Tight Approximation of 2D Bin Packing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Chips on wafers, or packing rectangles into grids
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
On the complexity of sequential rectangle placement in IEEE 802.16/WiMAX systems
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Exact algorithms for the two-dimensional guillotine knapsack
Computers and Operations Research
Tight Approximation Algorithms for Maximum Separable Assignment Problems
Mathematics of Operations Research
Online removable square packing
WAOA'05 Proceedings of the Third international conference on Approximation and Online 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
Approximating the orthogonal knapsack problem for hypercubes
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
A 3-approximation algorithm for two-dimensional bin packing
Operations Research Letters
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
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We consider the following rectangle packing problem: Given a set of rectangles, each of which is associated with a profit, we are requested to pack a subset of the rectangles into a bigger rectangle to maximize the total profit of rectangles packed. The rectangles may not overlap and may or may not be rotated. This problem is strongly NP-hard even for packing squares with identical profits. A simple (3 + ε)-approximation algorithm is presented. We further improve the algorithm by showing a worst-case ratio of at most 5/2 + ε. Finally we devise a (2 + ε)-approximation algorithm. A number of restricted cases are also considered.