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Optimal Packing of High-Precision Rectangles

Last modified: 2011-07-05

#### Abstract

The rectangle-packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, a problem for the previous state-of-the-art, which enumerates all locations for placing rectangles. We instead limit these locations and bounding box dimensions to the set of subset sums of the rectangles' dimensions, allowing us to test 4,500 times fewer bounding boxes and solve N=9 over two orders of magnitude faster. Finally, on the open problem of the feasibility of packing a specific infinite series of rectangles into the unit square, we pack the first 50,000 such rectangles and conjecture that the entire infinite series can fit.

#### Keywords

constraint satisfaction; rectangle packing; search; scheduling

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