Jim Gray, María A. Nieto-Santisteban, and Alexander S. Szalay
Zones index an N-dimensional Euclidian or metric space to efficiently support points-near-a-point queries either within a dataset or between two datasets. The approach uses relational algebra and the B-Tree mechanism found in almost all relational database systems. Hence, the Zones Algorithm gives a portable-relational implementation of points-near-point, spatial cross-match, and self-match queries. This article corrects some mistakes in an earlier article we wrote on the Zones Algorithm and describes some algorithmic improvements. The Appendix includes an implementation of point-near-point, self-match, and cross-match using the USGS city and stream gauge database.