Range Quantile Queries: Another Virtue of Wavelet Trees

Authors:
Travis Gagie;Simon J. Puglisi;Andrew Turpin
Affiliations:
Research Group for Combinatorial Algorithms in Bioinformatics, Bielefeld University, Germany;School of Computer Science and Information Technology, Royal Melbourne Institute of Technology, Australia;School of Computer Science and Information Technology, Royal Melbourne Institute of Technology, Australia
Venue:
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Year:
2009

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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 .