Fully Dynamic Spatial Approximation Trees

Gonzalo Navarro and Nora Reyes

The Spatial Approximation Tree (sa-tree) is a recently proposed data structure for searching in metric spaces. It has been shown that it compares favorably against alternative data structures in spaces of high dimension or queries with low selectivity. Its main drawbacks are: costly construction time, poor performance in low dimensional spaces or queries with high selectivity, and the fact of being a static data structure, that is, once built, one cannot add or delete elements. These facts rule it out for many interesting applications.

In this paper we overcome these weaknesses. We present a dynamic version of the sa-tree that handles insertions and deletions, showing experimentally that the price of adding dynamism is rather low. This is remarkable by itself since very few data structures for metric spaces are fully dynamic. In addition, we show how to obtain large improvements in construction and search time for low dimensional spaces or highly selective queries. The outcome is a much more practical data structure that can be useful in a wide range of applications.