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Given n points randomly distributed in [0,1] × [0,1], I try to allot to each point the area of the points which are closest to that point.
More formally as follows:
Given n points (x1, x2, … xn) in [0,1] × [0,1], assign to each xj a value equal to the measure of the set of points { z | d(z, xj) ≤ d(z, xi) } for all i in (1, 2, .. n).
I can’t come up with anything remotely efficient. Any help?
Sounds like you’re looking for Fortune’s algorithm for generating Voronoi diagrams.