Faster Wavelet Tree Queries

Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in compression, computational geometry, and most notably pattern matching in the form of the backward search—the backbone of many compressed full-text indices. Currently, in practice, for text over non-binary alphabets, the wavelet tree is probably the most used data structure for rank and select queries. Our improved wavelet tree representation and predictive model allows us to speed up queries by a factor of 2–3.