A study on the n-dimensional quadtree decomposition

We have examined the problem of the number of quad-tree blocks that an n-dimensional rectangle will be decomposed into on the average. The contribution of this paper are both practical and theoretical. From the practical point of view, the number of quadtree blocks of a decomposition is important, because it determines the number of nodes that a main-memory based quadtree will require; the number of entries in a linear quadtree that will be required ; also, the number of prices that a range query will be decomposed into which will be proportional to the response time for this query.