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Relative Neighbourhood Graph

Discussion in 'Mathematics' started by Alexander Giles, Oct 8, 2018.

  1. Is there some way to efficiently compute the relative neighbourhood graph on $n$ Euclidean points in $\mathbb{R}^{d}$?

    Though one can simply define

    MaxDist[x_, y_, point_] := Max[{EuclideanDistance[x, y],
    EuclideanDistance[x, point],
    EuclideanDistance[point, y]}]


    and then use it on every ${n \choose 3}$ triple of points to determine if, among all possible alternatives, the link is shortest, perhaps a nicer method is available using a matrix of Euclidean distances?

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