Foundations of Nearest Neighbor Queries in Euclidean Space

A number of approaches to computing nearest neighbor queries in Euclidean space are presented. This includes the depth-first and best-first methods as well as a comparison. The best first method is shown to be capable of being extended to report the neighboring objects in increasing order from the query object so that the search can be incremental and there is no need to know the value of k in advance. The incremental algorithm is shown to be modifiable to also work for objects that have spatial extent instead of being restricted to be point objects. The best-first method is also shown to yield the k approximate nearest neighbors give an error tolerance value.