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1, March 2005. 52 • D. Papadias et al. Fig. 5. Recursion tree. space. Lets call such a query empty, to distinguish it from nonempty queries that return results, each spawning d new recursive applications of the algorithm (where d is the dimensionality of the data space). Figure 5 shows a query processing tree, where empty queries are illustrated as transparent cycles. For the second level of recursion, for instance, the second query does not return any results, in which case the recursion will not proceed further.