LZBE: an LZ-style compressor supporting $O(\log n)$-time random access

TL;DR

This paper introduces LZBE, a new LZ-like compression scheme supporting efficient random access in logarithmic time, and demonstrates its advantages over existing methods in terms of expressiveness and access speed.

Contribution

The paper proposes LZBE, a novel LZ-like compression variant with structural restrictions that enable linear-time greedy factorization and efficient random access, surpassing previous schemes.

Findings

LZBE can be computed in linear time using a greedy approach.

LZBE is more expressive than the smallest grammar for certain strings.

Supports O(log n)-time random access with space linear in compressed size.

Abstract

An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the compressed size, no comparable guarantees are known for general LZ-like factorizations. This limitation motivated restricted variants such as LZ-End [Kreft and Navarro, 2013] and height-bounded LZ (LZHB) [Bannai et al., 2024], which trade off some compression efficiency for faster access. In this paper, we introduce LZ-Begin-End (LZBE), a new LZ-like variant in which every copy factor must refer to a contiguous sequence of preceding factors. This structural restriction ensures that any context-free grammar can be transformed into an LZBE factorization of the same size. We further study the greedy LZBE factorization, which selects each copy factor to be as long as possible while processing the input from left to right, and show that it can be computed in linear time. Moreover, we exhibit a family of strings for which the greedy LZBE factorization is asymptotically smaller than the smallest grammar. These results demonstrate that the LZBE scheme is strictly more expressive than grammar-based compression in the worst case. To support fast queries, we propose a data structure for LZBE-compressed strings that permits O(log n)-time random access within space linear in the compressed size, where n is the length of the input string.