A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
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
An asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Three-dimensional packings with rotations
Computers and Operations Research
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
SIAM Journal on Computing
Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing
Computers and Operations Research
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
A (2+ε)-approximation for scheduling parallel jobs in platforms
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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In the three dimensional strip packing problem, we are given a set of three-dimensional rectangular items I = {(xi, yi, zi) : i = 1, ..., n} and a three dimensional box B. The goal is to pack all the items in the box B without any overlap, such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of B and cannot be rotated. Building upon Caprara's work [4] for the two dimensional bin packing problem we obtain an approximation algorithm with a similar performance guarantee of T∞ ≈ 1.69 where T∞ is the well known Harmonic number that occurs naturally in the context of bin packing. The previously known approximation algorithms for this problem had worst case performance guarantees of 2 [7], 2.64 [14], 2.67 [15], 2.89 [10] and 3.25 [11]. Our second algorithm is an asymptotic PTAS for the case in which all items have square bases.