  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.
