I want to search many times, not identical elements but similar, for something a similar image or fingerprint without having to search the whole space. When I have a 1D case I sort it first. For 2D I can make boxes big enough to be not wasted on boxes containing no elements, these boxes have subboxes and these have elements.
There is a problem: because when the width is 100, then if I'm looking for a 401 I can find a 490 and I can't find a close element 399. You would have to look in the boxes around, in 9 instead of in one. It's still possible, but for 3D it will be 27, generally 3^n, what if we have 512D?