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Find the diameter of the set of n points in d-dimensional space

I am interested in finding the diameter of two sets of points in 128 dimensions. The first has 10,000 points and the second has 1,000,000. For this reason, I would like to do something better than the naive approach that takes O (n²). The algorithm will be able to handle any number of points and sizes, but at present I am very interested in these two specific data sets.

I am very interested in getting speed over accuracy, so based on this , I would find the (approximate) bounding box of the set of points, calculating the min and maximum value for each coordinate, so the time is O (n * d). Then , if I find the diameter of this window, the problem is solved .

In the 3d case, I could find the diameter of one side, since I know two edges, and then I could apply the Pythagorean theorem on the other, vertical in that side. I am not sure about this, but, of course, I don’t see how to generalize it to d-sizes.

An interesting answer can be found here , but it seems specific to 3 dimensions, and I want to use the method for d-measurements.

Interesting article: On calculating the diameter of a point set in multidimensional Euclidean space. Link . However, the implementation of the algorithm seems too much to me at this point.

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3 answers

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