Approximate Nearest Neighbor Queries Revisited

This paper proposes new methods to answer approximate nearest neighbor queries on a set of n points in d-dimensional Euclidean space. For any xed constant d, a data structure with O("(1;d)=2 n logn) preprocessing time and O("(1;d)=2 logn) query time achieves approximation factor 1+" for any given 0 < " < 1 a variant reduces the "-dependence by a factor of ";1=2 . For any arbitrary d, a data structure with O(d2 n logn) preprocessing time and O(d2 logn) query time achieves approximationfactor O(d3=2 ). Applications to various proximity problems are discussed.

• Type: Conference
• Year: 1997
• Where: COMPGEOM
• Authors: Timothy M. Chan
• Keywords: Approximate Nearest Neighbor, COMPGEOM 1997, Discrete Geometry, Query Time, Time Achieves Approximation