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A bisector tree allows to do fast but exact nearest neighbor searches in any space provided that you can measure the distance between any two points in that space. A bisector tree also allows fast neighbor searches (range queries/ finding all points within a given tolerance from your query point). Cf. this article for details: 'A Data Structure and an Algorithm for the Nearest Point Problem'; Iraj Kalaranti and Gerard McDonald. ieeexplore.ieee.org/iel5/32/35936/01703102.pdf