Wavelet Forests Revisited

TL;DR

This paper extends wavelet forests to support select queries efficiently, demonstrating practical performance improvements and analyzing parameter effects through experiments.

Contribution

It introduces support for select queries in wavelet forests with minimal space overhead, enhancing their practical applicability.

Findings

Wavelet forests can support select queries with little additional space.

Experiments show wavelet forests outperform standalone wavelet trees in many cases.

Parameter choices significantly affect select-query performance.

Abstract

Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this paper, we study wavelet forests, that is, wavelet-tree structures based on the fixed-block compression boosting technique. Such structures partition the input sequence into fixed-size blocks and build a separate wavelet tree for each block. Previous work showed that this approach yields strong practical performance for rank queries. We extend wavelet forests to support select queries. We show that select support can be added with little additional space overhead and that the resulting structures remain practically efficient. In experiments on a range of non-repetitive and repetitive inputs, wavelet forests are competitive with, and in most cases outperform, standalone wavelet-tree implementations. We also study the effect of internal parameters, including superblock size and navigational data, on select-query performance.