Practical and Space-Efficient LZ77 and LZ Pre-Compression via String Synchronizing Sets

Abstract

The Lempel-Ziv (LZ77) factorization decomposes a text into the least possible number $z$ of phrases that each refer to an earlier occurrence. It is this phrase count, rather than the encoded size, that governs the size of LZ-based compressed indexes, and computing a factorization with few phrases is a time and space bottleneck in their construction. In practice, computing LZ77 quickly has so far required building a suffix array. Ellert [SPIRE 2023] gave algorithms that compute the exact LZ77 factorization, and a 3-approximation of it, in sublinear working space. They have remained unimplemented, because two of their components resist a direct implementation: a lookup table that degenerates to patterns of length at most two for realistic inputs, and an orthogonal range reporting data structure that is impractical. We replace both, fine-tune every remaining stage, and obtain the first practical implementation, which runs in space close to the text rather than to the suffix array. On one thread, our 3-approximation factorizes 12-19x faster than the classical LPF algorithm while using 14x less memory; on 32 threads, even our exact algorithm is 1.4--2.9x faster than parallel LPF, at 9x less memory. In practice the approximation ratio stays far below 3. As a side result, passing only its perfect phrases to a downstream compressor yields a precompressor that is on par with the state of the art [Dinklage, SEA 2026] in compression ratio, and better in memory consumption and parallel throughput.

17 pages, 6 figures, 4 tables. Accepted at ALENEX 2027. Code: https://github.com/LukasNalbach/lz77-sss