Efficient Dynamic Compressed Data Structure for Suffix Array Queries and Updates

Core Concepts

We present the first dynamic compressed data structure that supports suffix array (SA) queries and updates in polylogarithmic time and δ-optimal space, where δ is a measure of string repetitiveness. The data structure also supports essential queries for realizing suffix trees, including inverse suffix array (ISA), random access (RA), and longest common extension (LCE) queries.

Abstract

The content discusses the development of an efficient dynamic compressed data structure that supports various string queries, with a focus on the suffix array (SA) query.
Key highlights:

The data structure supports SA queries, updates, ISA queries, RA queries, and LCE queries in polylogarithmic time using expected δ-optimal space, where δ is a measure of string repetitiveness.
The data structure is built using a randomized algorithm based on the restricted recompression technique, which constructs a derivation tree from the input string.
The authors introduce novel concepts such as interval attractors, restricted suffix count (RSC) queries, and restricted suffix search (RSS) queries to efficiently answer SA queries.
The update operation is achieved by modifying the directed acyclic graph (DAG) representation of the derivation tree and the weighted points representing non-periodic interval attractors.
The expected space complexity of the data structure is O((H + δ log n log σ/δ log n)B) bits, where H is the height of the derivation tree, n is the length of the input string, σ is the alphabet size, and B is the machine word size.
The time complexity for SA and ISA queries is O(H^3 log^2 n + H log^6 n) and O(H^3 log n + H log^4 n), respectively, where H = O(log n) with high probability.

The content provides a comprehensive and detailed summary of the proposed dynamic compressed data structure, its key components, and the theoretical guarantees on its performance and space efficiency.

Stats

None.

Quotes

None.

Key Insights Distilled From

Dynamic Suffix Array in Optimal Compressed Space

by Takaaki Nish... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2404.07510.pdf

Deeper Inquiries

How can the proposed dynamic compressed data structure be extended or adapted to support other string processing tasks beyond suffix array queries and updates

The proposed dynamic compressed data structure can be extended to support various other string processing tasks beyond suffix array queries and updates. One potential extension could be incorporating functionality for substring search and retrieval. By enhancing the data structure to efficiently locate and extract specific substrings within the compressed text, it could facilitate tasks such as pattern matching, text mining, and information retrieval. Additionally, the structure could be adapted to handle operations like substring concatenation, splitting, and manipulation, enabling a broader range of string processing tasks.

What are the potential practical applications of this dynamic compressed data structure, and how might it impact real-world problems that involve large, highly repetitive textual datasets

The dynamic compressed data structure has significant practical applications across various domains. In bioinformatics, where large genomic sequences are prevalent, the structure could streamline DNA sequence analysis, genome comparison, and mutation detection. In natural language processing, it could enhance text indexing, search engines, and document clustering for handling vast amounts of textual data efficiently. Moreover, in data compression and storage systems, the structure could optimize memory usage and processing speed for compressing and querying extensive datasets. Overall, the structure's impact lies in its ability to accelerate data processing, reduce storage requirements, and enhance the scalability of applications dealing with large, repetitive textual datasets.

Are there any alternative approaches or techniques that could be explored to further improve the space and time efficiency of dynamic compressed data structures for string processing

To further improve the space and time efficiency of dynamic compressed data structures for string processing, exploring alternative approaches and techniques is crucial. One potential avenue is investigating advanced compression algorithms tailored specifically for highly repetitive strings. Techniques like grammar-based compression, entropy encoding, and dictionary-based compression could be optimized and integrated into the data structure to enhance compression ratios and reduce memory overhead. Additionally, leveraging parallel processing and distributed computing frameworks could boost the performance of dynamic operations on compressed data, enabling faster updates and queries. Furthermore, exploring hybrid data structures that combine the strengths of compressed and uncompressed representations could offer a balance between space efficiency and query speed, catering to diverse string processing requirements.