Biased Range Trees

Vida Dujmovic, School of Computer Science, Carleton

A data structure, called a biased range tree, is presented that preprocesses a set S of n points in the plane and a query distribution D for 2-sided orthogonal range 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).