AAAI Publications, Twenty-First International Joint Conference on Artificial Intelligence

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New Improvements in Optimal Rectangle Packing
Eric Huang, Richard E. Korf

Last modified: 2009-06-25


The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our algorithm picks the x-coordinates of all the rectangles before picking any of the y-coordinates. For the x-coordinates, we present a dynamic variable ordering heuristic and an adaptation of a pruning algorithm used in previous solvers. We then transform the rectangle packing problem into a perfect packing problem that has no empty space, and present inference rules to reduce the instance size. For the y-coordinates we search a space that models empty positions as variables and rectangles as values. Our solver is over 19 times faster than the previous state-of-the-art on the largest problem solved to date, allowing us to extend the known solutions for a consecutive-square packing benchmark from N=27 to N=32.


search; constraint satisfaction; rectangle packing; scheduling

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