Dynamic Range Reporting in External Memory

Abstract

In this paper we describe a dynamic external memory data structure that supports range reporting queries in three dimensions in $O({\log }_B^{2}N+\frac{k}{B})$ I/O operations, where $k$ is the number of points in the answer and $B$ is the block size. This is the first dynamic data structure that answers three-dimensional range reporting queries in ${\log }_B^{O(1)}N+O(\frac{k}{B})$ I/Os.