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Unformatted text preview: f(m):= runtime on m points Step 3: Dealing with the strip. (nlogn) f(n) = 2f(n/2) + O(nlogn) nlog 2 (n). g(m):= runtime on m presorted (by x and y) points g(m)=2g(m/2) + Step 3 f(m) = O(nlogn) + g(m) Lemma: If p 1 , p 2 , . .. p n are points in a vertical strip of width 2 , where = min dist between pairs on the same side of the strips midline, sorted by y coord, and if i, j such that p i p j < , then the closest such pair satisFes ij 16 Make a grid of side length /2 Key observation: 112 No grid cell contains more than one point. Diameter of a grid cell is /2* 2 113...
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 Spring '08
 KLEINBERG
 Algorithms

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