Sorted Range Reporting Revisited

TL;DR

This paper presents an improved data structure for 2D sorted range reporting that reduces query time significantly while maintaining efficient space usage, advancing the state of the art in the field.

Contribution

It introduces a new data structure with optimized query time for 2D sorted range reporting, surpassing previous results and matching the best for unsorted reporting.

Findings

Query time improved by a factor of O(lglg n)

Space complexity remains efficient at O(n lglg n) words

Matches the best known results for unsorted range reporting

Abstract

We consider the two-dimensional sorted range reporting problem. Our data structure requires O(n lglg n) words of space and O(lglg n + k lglg n) query time, where k is the number of points in the query range. This data structure improves a recent result of Nekrich and Navarro [8] by a factor of O(lglg n) in query time, and matches the state of the art for unsorted range reporting [1].