Approximate Nearest Neighbor Queries Revisited

Abstract.

This paper proposes new methods to answer approximate nearest neighbor queries on a set of n points in d -dimensional Euclidean space. For any fixed constant d , a data structure with O( $\varepsilon$ ^(1-d)/2 n log n) preprocessing time and O( $\varepsilon$ ^(1-d)/2log n) query time achieves an approximation factor 1+ $\varepsilon$ for any given 0 < $\varepsilon$ < 1; a variant reduces the $\varepsilon$ -dependence by a factor of $\varepsilon$ ^-1/2 . For any arbitrary d , a data structure with O(d ² n log n) preprocessing time and O(d ²log n) query time achieves an approximation factor O(d ^3/2 ) . Applications to various proximity problems are discussed.