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, e.g., 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. In this paper, we present techniques to speed up queries by a factor of two (access and select) up to three (rank), compared to the wavelet tree implementation contained in the widely used Succinct Data Structure Library (SDSL). To this end, we change the underlying tree structure from a binary tree to a 4-ary tree and reduce cache misses by approximating rank queries using a predictive model to prefetch all data required for the actual rank query.