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I am faced with a problem in which I have to determine weather a random point(Cartesian co-ordinate) is closer in range[euclidean distance] to a set 'N' of points.

I cannot use the following methods as time complexity will increase significantly ::

1.) Simple Euclid distance method.

2.) Angle method.

3.) Cannot use the help of centro id, as the threshold distance calculation increases time complexity.

Arg_Stack
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  • How often do you need to query the same set of points? If it is only once, you cannot get better than linear. If it is more, you can build an appropriate acceleration data structure for the set (e.g. a kd-tree). – Nico Schertler Feb 03 '17 at 13:51
  • you can use LSH (https://en.wikipedia.org/wiki/Locality-sensitive_hashing) if you want to find approximate nearest neighbors fast. – Sandipan Dey Feb 03 '17 at 21:26

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