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
Packing d-Dimensional Bins in d Stages
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
Absolute approximation ratios for packing rectangles into bins
Journal of Scheduling
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
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 (5/3 + ε)-approximation for strip packing
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximation algorithms for scheduling and packing problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
A Reinforced Tabu Search Approach for 2D Strip Packing
International Journal of Applied Metaheuristic Computing
A (5/3+ε )-approximation for strip packing
Computational Geometry: Theory and Applications
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We consider the two-dimensional bin packing and strip packing problem, where a list of rectangles has to be packed into a minimal number of rectangular bins or a strip of minimal height, respectively. All packings have to be non-overlapping and orthogonal, i.e., axis-parallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the approximation ratio of 2 which was established more than a decade ago. Moreover, we present a polynomial time approximation scheme ($\mathcal{PTAS}$) for strip packing where rotations by 90 degrees are permitted and an algorithm for two-dimensional bin packing with an absolute worst-case ratio of 2, which is optimal provided $\mathcal{P} \not= \mathcal{NP}$.