Lempel Ziv Computation In Small Space (LZ-CISS)

TL;DR

This paper introduces space-efficient algorithms for Lempel Ziv factorization that operate within near-linear space and time bounds, enabling practical processing of large texts over integer alphabets.

Contribution

It presents the first algorithms for Lempel Ziv factorization that use close to minimal space while maintaining reasonable time complexity.

Findings

Uses $(1+\epsilon) n ext{lg} n + O(n)$ bits of space

Achieves $O(n / ext{epsilon}^2)$ time complexity

Applicable to texts over integer alphabets

Abstract

For both the Lempel Ziv 77- and 78-factorization we propose algorithms generating the respective factorization using $(1+\epsilon) n \lg n + O(n)$ bits (for any positive constant $\epsilon \le 1$) working space (including the space for the output) for any text of size \$n\$ over an integer alphabet in $O(n / \epsilon^{2})$ time.