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arXiv · 2206.10675

Orthogonal dissection into few rectangles

David Eppstein
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Abstract

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two.

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David Eppstein. 2022-06-21. Orthogonal dissection into few rectangles. https://doi.org/10.1007/s00454-023-00614-w

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