, Volume 62, Issue 1-2, pp 21-37

Biased Range Trees

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A data structure, called a biased range tree, is presented that preprocesses a set S of n points in ℝ2 and a query distribution D for 2-sided orthogonal range counting queries (a.k.a. dominance counting queries). The expected query time for this data structure, when queries are drawn according to D, matches, to within a constant factor, that of the optimal comparison tree for S and D. The memory and preprocessing requirements of the data structure are  O(nlog n).