Faster Lightweight Lempel-Ziv Parsing

TL;DR

This paper introduces a faster algorithm for Lempel-Ziv decomposition that operates efficiently in terms of time and space, making it suitable for large-scale data compression tasks.

Contribution

It presents a novel algorithm achieving improved time complexity for Lempel-Ziv parsing with near-optimal space usage.

Findings

Achieves $O(n(\log \sigma + \log \log n))$ time complexity.

Uses $n\log \sigma + \epsilon n$ bits of space, close to the input size.

Applicable to large datasets with large alphabets.

Abstract

We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input string, and $\sigma$ is the alphabet size. The $n\log\sigma$ bits in the space bound are for the input string itself which is treated as read-only.