Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem

Details Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem

2011-11-16

arxiv.org/abs/1111.3715v1

Computer Science

Discrete Mathematics

11 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1107.4463

Scientific paper

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.

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