A Hybrid Pointerless Representation of Quadtrees for Efficient Processing of Window Queries

Efficient management of spatial data is becoming more and more important and for very large sets of 2-dimensional data, secondary memory data representations are required. An important class of queries for spatial data are those that extract a subset of the data: they are called window queries (also region or range queries). In this paper we propose and analyze the hybrid linear quadtree for the efficient secondary memory processing of three kinds of window queries, namely the exist, the report and the select query. In particular we show that it is possible to answer to all the above queries for multiple non-overlapping features with a number of accesses to secondary memory never greater than the number of pixels inside the window. More precisely, we prove that for a window of size n×n in a feature space (e.g., an image) of size T×T (e.g., pixel elements) using the hybrid linear quadtree the exist and report query can be answered with O(nlog r T) accesses to secondary storage, while the select query can be answered with O(nlog r T+n2/r) accesses to secondary storage. This is an improvement in worstcase time complexity over previous results [Nar93] and shows that multiple nonoverlapping features (i.e., coloured images) can be treated with the same I/O complexity as single features (i.e., black and white images).