We are given a set P = p1, p2, ... , pN of N points in a plane. A Voronoi diagramis a

Chapter 10, Problem 10.51

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We are given a set P = p1, p2, ... , pN of N points in a plane. A Voronoi diagramis a partition of the plane into N regions Ri such that all points in Ri are closerto pi than any other point in P. Figure 10.78 shows a sample Voronoi diagramfor seven (nicely arranged) points. Give an O(N logN) algorithm to construct theVoronoi diagram.

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