An optimal algorithm for rectangle placement

Authors:
Patrick Healy;Marcus Creavin;Ago Kuusik
Affiliations:
Department of Computer Science and Information Systems, University of Limerick, Limerick, Ireland;Department of Computer Science and Information Systems, University of Limerick, Limerick, Ireland;Department of Computer Science and Information Systems, University of Limerick, Limerick, Ireland
Venue:
Operations Research Letters
Year:
1999

Citing 4
Cited 8

Computational geometry: an introduction

Computational geometry: an introduction
Fast algorithms for computing the largest empty rectangle

SCG '87 Proceedings of the third annual symposium on Computational geometry
Efficient algorithms for the largest rectangle problem

Information Sciences: an International Journal
The Bottomn-Left Bin-Packing Heuristic: An Efficient Implementation

IEEE Transactions on Computers

Generating optimal T-shape cutting patterns for circular blanks

Computers and Operations Research
Heuristic to optimize L-guillotine cutting operations

Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Case Study on Optimization of Rectangular Object Layout by Genetic Algorithm

Computer Supported Cooperative Work in Design IV
Solving the packing problem of rectangles with improved genetic algorithm based on statistical analysis

Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation
Two natural heuristics for 3D packing with practical loading constraints

PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Optimal algorithms for two-dimensional box placement problems

IEA/AIE'11 Proceedings of the 24th international conference on Industrial engineering and other applications of applied intelligent systems conference on Modern approaches in applied intelligence - Volume Part II
A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem

Journal of Combinatorial Optimization
A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP

Computers and Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the problem of placing efficiently a rectangle in a two-dimensional layout that may not have the bottom-left placement property. This problem arises when we apply any one of a number of iterative improvement algorithms to the cutting stock problem or its variants. Chazelle has given an O(n)-time placement algorithm when the layout has the bottom-left property; we extend this result to the more general situation by presenting a @Q(nlogn)-time algorithm