Journal of Parallel and Distributed Computing
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Fast Approximation Schemes for Two-Stage, Two-Dimensional Bin Packing
Mathematics of Operations Research
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved approximation algorithms for multidimensional bin packing problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
Inapproximability results for orthogonal rectangle packing problems with rotations
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
A 3-approximation algorithm for two-dimensional bin packing
Operations Research Letters
An approximation algorithm for square packing
Operations Research Letters
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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
Two-dimensional online bin packing with rotation
Theoretical Computer Science
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We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed non-overlapping and orthogonal, i.e., axis-parallel. We present an algorithm with an absolute worst-case ratio of 2 for the case where the rectangles can be rotated by 90 degrees. This is optimal provided $\mathcal{P}\not=\mathcal{NP}$ . For the case where rotation is not allowed, we prove an approximation ratio of 3 for the algorithm Hybrid First Fit which was introduced by Chung et al. (SIAM J. Algebr. Discrete Methods 3(1):66---76, 1982) and whose running time is slightly better than the running time of Zhang's previously known 3-approximation algorithm (Zhang in Oper. Res. Lett. 33(2):121---126, 2005).