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Consider a point set D with a measure function µ : D → R. Let A be the set of subsets of D induced by containment in a shape from some geometric family (e.g. axis-aligned rectangles, half planes, balls, k-oriented polygons). We say a range space (D, A) has an ε-approximation P if max R∈A µ(R ∩ P) µ(P) − µ(R ∩ D) µ(D) ≤ ε. We describe algorithms for(More)
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