We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings. Given a string of length n over an alphabet of size σ ≤ n, our method builds the wavelet tree in O(n log σ/ √ logn) time, improving upon the state-of-the-art algorithm by a factor of √ log n. As a consequence, given an array of n integers we c...