Space-efficient range reporting for categorical data

In the colored (or categorical) range reporting problem the set of input points is partitioned into categories and stored in a data structure; a query asks for categories of points that belong to the query range. In this paper we study two-dimensional colored range reporting in the external memory model and present I/O-efficient data structures for this problem. In particular, we describe data structures that answer three-sided colored reporting queries in O(K/B) I/Os and two-dimensional colored reporting queries in(log₂log_B N + K/B) I/Os when points lie on an N x N grid, K is the number of reported colors, and B is the block size. The space usage of both data structures is close to optimal.