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Window operations serve as the basis of a number of queries that can be posed in a spatial database. Examples of these window-based queries include the exist query (i.e., determining whether or not a spatial feature exists inside a window) and the report query, (i.e., reporting the identity of all the features that exist inside a window). Algorithms are described for answering window queries in &Ogr;(n log logT) time for a window of size n x n in a feature space (e.g., an image) of size T x T (e.g., pixel elements). The significance of this result is that even though the window contains n2 pixel elements, the worst-case time complexity of the algorithms is almost linearly proportional (and not quadratic) to the window diameter, and does not depend on other factors. The above complexity bounds are achieved via the introduction of the incomplete pyramid data structure (a variant of the pyramid data structure) as the underlying representation to store spatial features and to answer queries on them.

Efficient processing of window queries in the pyramid data structure