In this article we show that bottom-left guillotine placement of rectangles ordered by decreasing width in a fixed-width bin is not more than three times the height of an optimal placement. This bound is also true for bottom-left placement of rectangles without the guillotine constraints. Thus, bottom-left guillotine placement in which rectangles are ordered by decreasing width has the same worst case performance bound as bottom-left placement of rectangles without guillotine constraints.
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Girkar, M., Macleod, B. & Moll, R. Performance Bound for Bottom-Left Guillotine Packing of Rectangles. J Oper Res Soc 43, 169–175 (1992). https://doi.org/10.1057/jors.1992.21
- Bottom-Left Packing of Rectangles
- Guillotine Placement
- Worst Case Performance Bound