Wavelet Forests Revisited

2026-04-13

AI Summary

This work addresses the problem of efficiently supporting select queries on sequences with minimal space overhead. To this end, the authors propose a wavelet forest structure enhanced by fixed-block compression, wherein an individual wavelet tree is constructed for each data block. This approach uniquely extends select functionality to such block-wise wavelet trees for the first time. The design incurs almost no additional space cost while significantly improving query performance through optimized navigation data structures. Experimental results demonstrate that the proposed wavelet forest achieves select query performance that is either superior or comparable to conventional wavelet tree implementations across a variety of datasets, including both repetitive and non-repetitive sequences.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Distributed Search
• Machine Learning: Dimensionality Reduction/Feature Selection

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• wavelet forests
• select queries
• rank queries
• compressed data structures
• space-efficient indexing

Innovation

• wavelet forests
• select queries
• compression boosting
• rank queries
• space-efficient data structures