SIAM Journal on Computing
Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem
SIAM Journal on Computing
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximation schemes for multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New approximability and inapproximability results for 2-dimensional Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Harmonic algorithm for 3-dimensional strip packing problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Three-dimensional packings with rotations
Computers and Operations Research
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
Approximation algorithms for 3D orthogonal Knapsack
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing
Computers and Operations Research
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
Approximation algorithms for multiple strip packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
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We present an asymptotic (2 + ε)-approximation algorithm for the 3D-strip packing problem, for any ε 0. In the 3D-strip packing problem the input is a set L = {b1, b2,. . ., bn} of 3-dimensional boxes. Each box bi has width, length, and height at most 1. The problem is to pack the boxes into a 3-dimensional bin B of width 1, length 1 and minimum height, so that the boxes do not overlap. We consider here only orthogonal packings without rotations; this means that the boxes are packed so that their faces are parallel to the faces of the bin, and rotations are not allowed. This algorithm improves on the previously best algorithm of Miyazawa and Wakabayashi which has asymptotic performance ratio of 2.64. Our algorithm can be easily modified to a (4 + ε)-approximation algorithm for the 3D-bin packing problem.