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
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On packing squares with resource augmentation: maximizing the profit
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
An efficient approximation for the generalized assignment problem
Information Processing Letters
An optimal bound for two dimensional bin packing
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Resource augmentation in two-dimensional packing with orthogonal rotations
Operations Research Letters
Two-dimensional bin packing with one-dimensional resource augmentation
Discrete Optimization
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We study the following square packing problem: Given a set $Q$ of squares with positive profits, the goal is to pack a subset of $Q$ into a rectangular bin $\mathcal R$ so that the total profit of the squares packed in $\mathcal R$ is maximized. Squares must be packed so that their sides are parallel to those of $\mathcal R$. We present a polynomial time approximation scheme for the problem, which for any value $\epsilon 0$ finds and packs a subset $Q' \subseteq Q$ of profit at least $(1-\epsilon) OPT$, where $OPT$ is the profit of an optimum solution.