Abstract
We consider the following problem: given a rectangle containingn points, find the largest perimeter subrectangle whose sides are parallel to those of the original rectangle, whose aspect ratio is below a given bound, and which does not contain any of the given points. Chazelle, Drysdale and Lee have studied a variant of this problem with areas as the quantity to be maximized. They gave anO(nlog3 n) algorithm for that problem. We adopt a similar divide-and-conquer approach and are able to use the simpler properties of the perimeter measure to obtain anO(nlog2 n) algorithm for our problem.
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