A polynomial time approximation scheme for the square packing problem

Authors:
Klaus Jansen;Roberto Solis-Oba
Affiliations:
Institut für Informatik, Universität zu Kiel, Kiel, Germany;Department of Computer Science, The University of Western Ontario, London, Canada
Venue:
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Year:
2008

Citing 8
Cited 6

Packing squares into a square

Journal of Parallel and Distributed Computing
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem

Mathematics of Operations Research
An efficient approximation for the generalized assignment problem

Information Processing Letters
Maximizing the Total Profit of Rectangles Packed into a Rectangle

Algorithmica
An optimal bound for two dimensional bin packing

SFCS '75 Proceedings of the 16th 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

Two for One: Tight Approximation of 2D Bin Packing

WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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
2D knapsack: packing squares

FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Packing anchored rectangles

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
2D knapsack: Packing squares

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a set Q of squares with positive profits, the square packing problem is to select and pack a subset of squares of maximum profit into a rectangular bin R. We present a polynomial time approximation scheme for this problem, that for any value Ɛ 0 finds and packs a subset Q′ ⊆ Q of profit at least (1 - Ɛ)OPT, where OPT is the profit of an optimum solution. This settles the approximability of the problem and improves on the previously best approximation ratio of 5/4 +Ɛ achieved by Harren's algorithm.