Range Quantile Queries: Another Virtue of Wavelet Trees
Abstract
We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient 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 coloured range reporting and document listing.
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