Bottom-Left Placement Theorem for Rectangle Packing
Discrete Mathematics
2011-07-25 v1 Computational Geometry
Data Structures and Algorithms
Abstract
This paper proves a bottom-left placement theorem for the rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given rectangles into a rectangular container without overlapping, then we can achieve a feasible packing by successively placing a rectangle onto a bottom-left corner in the container. This theorem shows that even for the real-parameter rectangle packing problem, we can solve it after finite times of bottom-left placement actions. Based on this theorem, we might develop efficient heuristic algorithms for solving the rectangle packing problem.
Cite
@article{arxiv.1107.4463,
title = {Bottom-Left Placement Theorem for Rectangle Packing},
author = {Wenqi Huang and Tao Ye and Duanbing Chen},
journal= {arXiv preprint arXiv:1107.4463},
year = {2011}
}