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I found that Weighted nearest neighbor voronoi diagrams are widely studied and there are optimal algorithms for that.

But I could not find anything on Weighted furthest point voronoi diagrams !! But it is very unlikely that this version of voronoi diagrams are not studied before.

So, any link / reference will be helpful.

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There's something on the multiplicatively weighted farthest neighbor query problem (but not on the associated Voronoi diagram) in my paper

Approximate weighted farthest neighbors and minimum dilation stars. J. Augustine, D. Eppstein, and K. Wortman. arXiv:cs.CG/0602029. Proc. 16th Annual International Computing and Combinatorics Conference (COCOON 2010), Nha Trang, Vietnam. Lecture Notes in Comp. Sci. 6196, Springer-Verlag, 2010, pp. 90-99. Discrete Mathematics, Algorithms and Applications 2(4): 553-656, 2010.

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