Efficient range searching for categorical and plain data

Abstract

In the orthogonal range-searching problem, we store a set of input points S in a data structure; the answer to a query Q is a piece of information about points in Q ∩ S , for example, the list of all points in Q ∩ S or the number of points in Q . In the colored (or categorical) range-searching problem, the set of input points is partitioned into categories; the answer to a query is a piece of information about categories of points in a query range. In this article, we describe several new results for one- and two-dimensional range-searching problems. We obtain an optimal adaptive data structure for counting the number of objects in a three-sided range and for counting categories of objects in a one-dimensional range. We also obtain new results on color range reporting in two dimensions, approximate color counting in one dimension, and some other related problems.