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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Approximating the orthogonal knapsack problem for hypercubes
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Two-dimensional bin packing with one-dimensional resource augmentation
Discrete Optimization
Packing Rectangles into 2OPT Bins Using Rotations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Two for One: Tight Approximation of 2D Bin Packing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical 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
A note on the Kenyon-Remila strip-packing algorithm
Information Processing Letters
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
Absolute approximation ratios for packing rectangles into bins
Journal of Scheduling
A(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Coordination mechanisms for selfish parallel jobs scheduling
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Smart-Grid electricity allocation via strip packing with slicing
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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The strip packing problem is to pack a set of rectangles into a strip of fixed width and minimum length. We present asymptotic polynomial time approximation schemes for this problem without and with 90° rotations. The additive constant in the approximation ratios of both algorithms is 1, improving on the additive term in the approximation ratios of the algorithm by Kenyon and Rémila (for the problem without rotations) and Jansen and van Stee (for the problem with rotations), both of which have a larger additive constant O(1/ε2), ε 0. The algorithms were derived from the study of the rectangle packing problem: Given a set R of rectangles with positive profits, the goal is to find and pack a maximum profit subset of R into a unit size square bin [0, 1] × [0, 1]. We present algorithms that for any value ∈ 0 find a subset R′ ⊆ R of rectangles of total profit at least (1 - ∈)OPT, where OPT is the profit of an optimum solution, and pack them (either without rotations or with 90° rotations) into the augmented bin [0, 1]×[0,1+∈].