English

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

R2 v1 2026-06-21T19:36:45.391Z