(1+ε)-approximate nearest neighbor search

(1+$ε$)-approximate nearest neighbor search is a variant of the nearest neighbor search problem. A solution to the (1+$ε$)-approximate nearest neighbor search is a point or multiple points within distance (1+$ε$) $R$ from a query point, where $R$ is the distance between the query point and its true nearest neighbor.

Reasons to approximate nearest neighbor search include the space and time costs of exact solutions in high-dimensional spaces (see curse of dimensionality) and that in some domains, finding an approximate nearest neighbor is an acceptable solution.

Approaches for solving (1+$ε$)-approximate nearest neighbor search include kd-trees, Locality Sensitive Hashing and brute force search.