Published on *Computer Science Department at Princeton University* (http://www.cs.princeton.edu)

This paper investigates the existence of linear space data structures for range searching. We examine the homothetic range search problem, where a set S of n points in the plane is to be preprocessed so that for any triangle T with sides parallel to three fixed directions the points of S that lie in T can be

computed efficiently. We also look at domination earching in three dimensions. In this problem, S is a set of n points in E3 and the question is to retrieve all points of S that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the

first case and nearly optimal in the second.