Achieving Spatial Adaptivity while Finding Approximate Nearest Neighbors

We present the first spatially adaptive data structure that answers approximate nearest neighbor (ANN) queries to points that reside in a geometric space of any constant dimension d. The Lt-norm approximation ratio is O(d1+1/t ), and the running time for a query q is O(d2 lg (p, q)), where p is the result of the preceding query and (p, q) is the number of input points in a suitably-sized box containing p and q. Our data structure has O(dn) size and requires O(d2 n lg n) preprocessing time, where n is the number of points in the data structure. The size of the bounding box for depends on d, and our results rely on the Random Access Machine (RAM) model with word size (lg n).

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Jonathan Derryberry, Don Sheehy, Maverick Woo, Danny Dominic Sleator
• Keywords: Approximate Nearest Neighbor, CCCG 2008, Computational Geometry, Data Structure, Lg N