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Corner occupying theorem for the two-dimensional integral rectangle packing problem
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DOI：10.1007/s11432-012-4702-8.png)
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Abstract
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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 a 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:
rectangle packing
bottom-left
corner occupying theorem
NP hard
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