Space Efficient Linear Time Lempel-Ziv Factorization on Constant~Size~Alphabets

TL;DR

This paper introduces a space-efficient linear-time algorithm for Lempel-Ziv factorization on constant size alphabets, significantly reducing memory usage while maintaining competitive speed.

Contribution

The authors develop a novel linear-time LZ77 factorization algorithm that uses only N log N + O(1) bits of space for constant alphabets, improving upon previous methods.

Findings

Uses only N log N + O(1) bits of space for constant alphabets

Achieves linear time complexity comparable to previous algorithms

Experimental results show only about twice slower speed than fastest existing methods

Abstract

We present a new algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length $N$ in linear time, that utilizes only $N\log N + O(1)$ bits of working space, i.e., a single integer array, for constant size integer alphabets. This greatly improves the previous best space requirement for linear time LZ77 factorization (K\"arkk\"ainen et al. CPM 2013), which requires two integer arrays of length $N$. Computational experiments show that despite the added complexity of the algorithm, the speed of the algorithm is only around twice as slow as previous fastest linear time algorithms.