An Investigation of Grid-enabled Tree Indexes for Spatial Query Processing

Abstract

Two-dimensional tree-based spatial indexes (e.g., the quad tree or the k-d tree) are commonly used for indexing spatial data. However, both types of indexes have limitations. Although two-dimensional trees can handle skewed data, index traversal and tree maintenance can be expensive. In contrast, a spatial grid has low update overhead, but is not suitable for skewed data. In this paper, we investigate the augmentation of a grid into tree-based indexing for spatial query processing. We introduce the Grid-Enabled Tree index (the GE-Tree, for short); a hybrid spatial index that augments a grid into two-dimensional tree indexes. In particular, we investigate the use of a grid at the leaf level of a quadtree to facilitate tree navigation and maintenance. At the expense of the extra storage, the GE-Tree achieves constant-time tree search, insert, update, and leaf node neighbor finding operations, in contrast to the log time in conventional two-dimensional trees, e.g., O(log S) in S ×S space as in the case of the quadtree. Also, we illustrate how the range and k-nearest-neighbor operations can be facilitated using grid-enabled trees. Experimental results using real spatial data highlight the tradeoffs of when using grid-enabled trees pay off in contrast to regular space-partitioning trees for range and k-NN operation. Also, the GE-Tree outperforms conventional tree or grid-only indexes by up to two times for leaf node access operations, e.g., as in point-location search, neighbor-finding search operations, and the k-nearest neighbor search.