Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Shelf algorithms for on-line strip packing
Information Processing Letters
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
Fast Approximation Schemes for Two-Stage, Two-Dimensional Bin Packing
Mathematics of Operations Research
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on 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
SIAM Journal on Computing
Exact algorithms for the two-dimensional guillotine knapsack
Computers and Operations Research
Two-dimensional bin packing with one-dimensional resource augmentation
Discrete Optimization
On the weak computability of a four dimensional orthogonal packing and time scheduling problem
Theoretical Computer Science
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The 2-dimensional Bin Packing problem (2BP) is a generalization of the classical Bin Packing problem and is defined as follows: Given a collection of rectangles specified by their width and height, oack: these into minimum number of squares bins of units size. We study the case of "orthogonal packing without rotations", where rectangles cannot be rotated and must be packed parallel to the edges of a bin.Often in practical cases of 2BP problems there are additional constraints on how complicated the packing patterns in a bin can be. A well-studied and frequently used constraint is that every rectangle in the packing must be obtainable by recursively applying a sequence of edge-to-edge cuts parallel to the edge of the bin. Such cuts are known as guillotine cuts. Our main results is that the guillotine 2BP problem admits an asymptotic polynomial time approximation scheme. This is sharp contrast with the fact that the general 2BP problem is APX-Hard. En route to our main result, we show a structural theorem about approximating general guilootine packings by simpler packings, which could be of independent interest.