LZ78 Substring Compression in Compressed Space

TL;DR

This paper explores indexing techniques for LZ78-based data compression, enabling fast substring factorization in compressed space with a logarithmic slowdown, which enhances data processing efficiency.

Contribution

It introduces an algorithm for LZ78 factorization in the substring compression model that operates in compressed space with logarithmic time complexity overhead.

Findings

Efficient indexing of compressed data for LZ78 factorization.

Algorithm achieves logarithmic slowdown in factorization time.

Supports fast substring queries in compressed space.

Abstract

The Lempel--Ziv 78 (LZ78) factorization is a well-studied technique for data compression. It and its derivatives are used in compression formats such as "compress" or "gif". Although most research focuses on the factorization of plain data, not much research has been conducted on indexing the data for fast LZ78 factorization. Here, we study the LZ78 factorization and its derivatives in the substring compression model, where we are allowed to index the data and return the factorization of a substring specified at query time. In that model, we propose an algorithm that works in compressed space, computing the factorization with a logarithmic slowdown compared to the optimal time complexity.