(α,β)-covered polygons have bounded doubling dimension and geodesically convex sets have perimeter O(diameter), enabling O(n + m log n) expected-time closest-pair algorithm.
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On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons
(α,β)-covered polygons have bounded doubling dimension and geodesically convex sets have perimeter O(diameter), enabling O(n + m log n) expected-time closest-pair algorithm.