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Packing Anchored Rectangles

Let S be a set of n points in the unit square [,1]2, one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cover at least a positive constant area (about .9). This is a first step towards the solution of a longstanding conjecture that the rectangles in such a packing can jointly cover an area of at least 1/2.

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