Biased Range Trees

A data structure, called a biased range tree , is presented that preprocesses a set S of n points in ℝ 2 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 ( n log n ).