Inverse rectangle in rectangle packing / covering algorithm

Asked Apr 08 '16 at 09:30

Active Apr 08 '16 at 09:30

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Traditionally a rectangle-in-rectangle packing problem has a set of rectangles with known,fixed sizes which you want to pack in a as small as possible outer rectangle.

I want to do the opposite. I have a fixed outer rectangle and a set of rectangles of which only aspect ratio must be preserved. I want to place the rectangles in the outer rectangle in such a way that as much space as possible is covered. Additionally, the rectangles have a relative weight assigned to them.

The application is to place pictures in a frame, where some pictures must be larger than others. We want to cover as much as possible of the frame.

Anybody who can send me in the right direction or has some papers that may help? Thanks

asked Apr 08 '16 at 09:30

Seba Kerckhof

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What do the weights mean? – harold Apr 08 '16 at 09:38
To me it looks like a more complicated variant of the knapsack problem. Try to use that solution approach. – Davide Spataro Apr 08 '16 at 09:39
@harold the weights are the relative importance of each picture, or how big it should be compared to other pictures. – Seba Kerckhof Apr 11 '16 at 21:37
You can just pretend there is no scaling then. If you have any solution, you can convert it to fit the intended fixed boundary, just by scaling it afterwards. – harold Apr 12 '16 at 09:32

Inverse rectangle in rectangle packing / covering algorithm

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