Range Quantile Queries: Another Virtue of Wavelet Trees

TL;DR

This paper demonstrates how balanced wavelet trees can efficiently support range quantile queries, enabling applications like space-efficient coloured range reporting and document listing.

Contribution

It introduces a novel use of wavelet trees for range quantile queries and their application to related problems, enhancing efficiency and space usage.

Findings

Supports efficient range quantile queries

Enables space-efficient coloured range reporting

Facilitates document listing applications

Abstract

We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient {\em range quantile queries}. A range quantile query takes a rank and the endpoints of a sublist and returns the number with that rank in that sublist. For example, if the rank is half the sublist's length, then the query returns the sublist's median. We also show how these queries can be used to support space-efficient {\em coloured range reporting} and {\em document listing}.