Packing Rectangles into 2OPT Bins Using Rotations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Two for One: Tight Approximation of 2D Bin Packing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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
A polynomial time approximation scheme for the square packing problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
SIAM Journal on Computing
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
A (5/3 + ε)-approximation for strip packing
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Absolute approximation ratios for packing rectangles into bins
Journal of Scheduling
An approximation scheme for the two-stage, two-dimensional knapsack problem
Discrete Optimization
Theoretical Computer Science
A (5/3+ε )-approximation for strip packing
Computational Geometry: Theory and Applications
Hi-index | 0.00 |
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 so that the total profit of rectangles packed is maximized. The rectangles may not overlap. This problem is strongly NP-hard even for packing squares with identical profits. We first present a simple (3 + ε)-approximation algorithm. Then we consider a restricted version of the problem and show a (2 + ε)-approximation algorithm. This restricted problem includes the case where rotation by 90° is allowed (and is possible), and the case of packing squares. We apply a similar technique to the general problem, and get an improved algorithm with a worst-case ratio of at most 5/2 + ε. Finally, we devise a (2 + ε)-approximation algorithm for the general problem.