Models and algorithms for packing rectangles into the smallest square

DOI10.1016/j.cor.2015.04.024zbMath1349.68321OpenAlexW234647914MaRDI QIDQ342053

Silvano Martello, Michele Monaci

Publication date: 17 November 2016

Published in: Computers \& Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cor.2015.04.024

zbMATH Keywords

randomized algorithmmathematical modeltwo-dimensional packing

Mathematics Subject Classification ID

Integer programming (90C10) Approximation methods and heuristics in mathematical programming (90C59) Randomized algorithms (68W20) Combinatorial aspects of packing and covering (05B40)

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Cites Work

• Unnamed Item
• Optimal rectangle packing
• Packing into the smallest square: worst-case analysis of lower bounds
• Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet
• An analytical model for the container loading problem
• A lower bound for the non-oriented two-dimensional bin packing problem
• Worst-case analysis of fast heuristics for packing squares into a square
• An exact algorithm for general, orthogonal, two-dimensional knapsack problems
• Local search algorithms for the rectangle packing problem with general spatial costs
• A method of optimal lattice packing of congruent oriented polygons in the plane
• Optimizing the packing of cylinders into a rectangular container: A nonlinear approach
• Conflict analysis in mixed integer programming
• Resource augmentation in two-dimensional packing with orthogonal rotations
• An improved typology of cutting and packing problems
• The Bottomn-Left Bin-Packing Heuristic: An Efficient Implementation
• ENUMERATING BOTTOM-LEFT STABLE POSITIONS FOR RECTANGLE PLACEMENTS WITH OVERLAP
• An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure
• Algorithms for Unconstrained Two-Dimensional Guillotine Cutting
• Orthogonal Packings in Two Dimensions
• An Algorithm for Two-Dimensional Cutting Problems
• Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems
• The Three-Dimensional Bin Packing Problem
• Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes