Decomposing Polygons into Fat Components
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We study the problem of decomposing (i.e. partitioning and covering) polygons into components that are α-fat, which means that the aspect ratio of each subpolygon is at most α. We consider decompositions without Steiner points. We present a polynomial-time algorithm for simple polygons that finds the minimum α such that an α-fat partition exists. Furthermore, we show that finding an α-fat partition or covering with minimum cardinality is NP-hard for polygons with holes.
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