Wavelet trees have received significant attention due to their applications in compressed data structures. We present several work-efficient parallel algorithms for wavelet tree construction that have polylogarithmic span, improving upon the linear span of the recent parallel algorithms by Fuentes-Sepulveda et al. We experimentally show that on 40 cores our algorithms outperform the existing parallel algorithms by 2--12x and achieve up to 27x speedup over the sequential algorithm on a variety of real-world and artificial inputs. Our algorithms show good scalability with both increasing input size and increasing alphabet size. We also discuss how to extend our algorithms to variants of the standard wavelet tree.
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