A log log n data structure for three-sided range queries

Abstract

We present a data structure for three-sided range queries for a set of n points in R 2 where the x-coordinates of the points are restricteed to the range {1, 2, …, N}. The answer to a three-sided range query is the set of points lying in the semi-finite strip defined by three coordinates x 0, x 1 and y 0. The data structure is based on the priority search tree of McCreight (1981). The basic idea is to start the search at the leaves of the three and to reduce the query to a constant number of three-sided range queries on sets of O(log n) points. For this purpose we extend the basic priority search tree T by adding four secondary priority search trees to each search path in T. This extended priority search tree can answer three-sided range queries in O(log log n + k) time and O(N + n) space, (here, k is the cardinality of the answer).