Given a set S of s points in the plane, where do we place a new point, p, in order to maximize the area of its region in the Voronoi diagram of S and p? We study the case where the Voronoi neighbors of p are in convex position, and prove that there is at most one local maximum.

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Keywords Computational geometry, Locational planning, Optimization, Voronoi diagram
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Dehne, F, Klein, R. (Rolf), & Seidel, R. (Raimund). (2002). Maximizing a voronoi region: The convex case. doi:10.1007/3-540-36136-7_54