Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem
Discrete Mathematics
2011-11-17 v1 Combinatorics
Optimization and Control
Abstract
This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container without overlapping, then we can achieve a feasible packing by successively placing an integral rectangle onto a bottom-left corner in the container. Based on this theorem, we might develop efficient heuristic algorithms for solving the integral rectangle packing problem. In fact, as a vague conjecture, this theorem has been implicitly mentioned with different appearances by many people for a long time.
Keywords
Cite
@article{arxiv.1111.3715,
title = {Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem},
author = {Wenqi Huang and Tao Ye and Duanbing Chen},
journal= {arXiv preprint arXiv:1111.3715},
year = {2011}
}
Comments
11 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1107.4463