Lempel-Ziv Computation In Compressed Space (LZ-CICS)

TL;DR

This paper presents efficient algorithms for computing Lempel-Ziv factorizations of texts in compressed space, achieving near-linear time with minimal working space, and leveraging compressed suffix tree representations for further optimization.

Contribution

It introduces algorithms for Lempel-Ziv 77- and 78-factorizations that operate in compressed space and near-linear time, improving efficiency over previous methods.

Findings

Lempel-Ziv factorizations can be computed in $O(n \, \lg \lg \sigma)$ time.

Using compressed suffix trees, factorizations can be computed in $O(n)$ time.

Algorithms use $O(n \lg \sigma)$ bits of space, optimizing memory usage.

Abstract

We show that both the Lempel Ziv 77- and the 78-factorization of a text of length $n$ on an integer alphabet of size $\sigma$ can be computed in $O(n \lg \lg \sigma)$ time (linear time if we allow randomization) using $O(n \lg \sigma)$ bits of working space. Given that a compressed representation of the suffix tree is loaded into RAM, we can compute both factorizations in $O(n)$ time using $z \lg n + O(n)$ bits of space, where $z$ is the number of factors.