Journal of Parallel and Distributed Computing
Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
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
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
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
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
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 asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Scheduling parallel jobs to minimize the makespan
Journal of Scheduling
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
Harmonic algorithm for 3-dimensional strip packing problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth 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
On efficient weighted rectangle packing with large resources
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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
Scheduling jobs on heterogeneous platforms
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
A (5/3 + ε)-approximation for strip packing
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A (2+ε)-approximation for scheduling parallel jobs in platforms
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
A (5/3+ε )-approximation for strip packing
Computational Geometry: Theory and Applications
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In the rectangle packing problem we are given a set R of rectangles with positive profits and the goal is to pack a subset of R into a unit size square bin [0,1]x[0,1] so that the total profit of the rectangles that are packed is maximized. We present algorithms that for any value @e0 find a subset R^'@?R of rectangles of total profit at least (1-@e)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]x[0,1+@e]. This algorithm can be used to design asymptotic polynomial time approximation schemes (APTAS) for the strip packing problem without and with 90^@? rotations. The additive constant in the approximation ratios of both algorithms is 1, thus improving on the additive term in the approximation ratios of the algorithm by Kenyon and Remila (for the problem without rotations) and Jansen and van Stee (for the problem with rotations), both of which have a much larger additive constant O(1/@e^2), @e0.