Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
New bounds for multi-dimensional packing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Approximation algorithms for multiple strip packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
A 3-approximation algorithm for two-dimensional bin packing
Operations Research Letters
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We present an asymptotic PTAS for Two-Dimensional Bin Packing, which requires packing (or cutting) a given set of rectangles from the minimum number of square bins, with the further restriction that cutting the rectangles from the bins can be done in two stages, as is frequently the case in real-world applications. To the best of our knowledge, this is the first approximation scheme for a nontrivial two-dimensional (and real-world) generalization of classical one-dimensional Bin Packing in which rectangles have to be packed in (finite) squares. A simplification of our method yields an asymptotic PTAS for the two-stage packing of rectangles in a bin of unit width and infinite height. Moreover, we point out that our method may lead to a better approximation guarantee for Two-Dimensional Bin Packing without stage restrictions, provided some structural property holds.