Translating Between Wavelet Tree and Wavelet Matrix Construction

TL;DR

This paper presents a method to efficiently convert between wavelet tree and wavelet matrix constructions without increasing asymptotic complexity, enhancing flexibility in their use for various applications.

Contribution

We develop a data structure that allows transforming construction algorithms between wavelet trees and matrices efficiently, preserving their asymptotic performance.

Findings

Conversion between wavelet structures is efficient and asymptotically optimal.

The method does not increase time or space complexity of existing algorithms.

This facilitates flexible use of wavelet structures in applications.

Abstract

The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 2015]) are compact data structures with many applications such as text indexing or computational geometry. By continuing the recent research of Fischer et al. [ALENEX, 2018], we explore the similarities and differences of these heavily related data structures with focus on their construction. We develop a data structure to modify construction algorithms for either the wavelet tree or matrix to construct instead the other. This modification is efficient, in that it does not worsen the asymptotic time and space requirements of any known wavelet tree or wavelet matrix construction algorithm.