Dynamic Range Reporting in External Memory

TL;DR

This paper introduces a novel dynamic external memory data structure for efficient three-dimensional range reporting queries, achieving optimal I/O performance with minimal overhead.

Contribution

It presents the first dynamic data structure for 3D range reporting that operates in logarithmic I/O complexity with respect to block size and data size.

Findings

Supports range reporting in 3D with optimal I/O complexity

First dynamic structure achieving these bounds in external memory

Operates efficiently with minimal I/O overhead for large datasets

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.