Fair splitting rule

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The fair rule chooses to split along the longest side of the node. On this axis it chooses to split at the midpoint of the minimum bounding interval of the contained points.

References

A decomposition of Multidimensional Point Sets with Applications to k-Nearest-Neighbors and n-Body Potential Fields, Paul B. Callahan, S. Rao. Kosaraju, Journal of the ACM, Volume 42, Number 1, pages 67-90, January 1995.

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Fair splitting rule