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This is a Quantitative Study study.

September 30, 2025Open Access

Minimum Partition of Polygons under Width and Cut Constraints

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This analysis reveals structural properties of polygon partitioning under width constraints, suggesting optimal cutting directions.

The minimum partition number of a simple polygon is greater than or equal to that of any subpolygon satisfying certain properties.
Each subpolygon must meet a width constraint based on the orthogonal projection onto unit vectors for effective partitioning.
An optimal partition for convex polygons can be identified along a specific direction using parallel cuts, computable in linear time.
A partition analogue of Bang's conjecture is proven, asserting relative widths of convex regions must total at least one.

Chung et al. (2025) studied this question.

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