Approximating LZ77 in Small Space

TL;DR

This paper presents a method to approximate the LZ77 compression of a string efficiently in small space, balancing time, I/O, and space complexity with a tunable parameter.

Contribution

It introduces an algorithm that constructs an LZ77-like parse with a controlled number of phrases using sub-quadratic space and near-linear time.

Findings

Achieves an LZ77-like parse with O(z/ε) phrases

Uses O(n^{1+ε}) time and I/Os for approximation

Operates within O(z/ε) space

Abstract

Given a positive \(\epsilon \leq 1\) and read-only access to a string \(S [1..n]\) whose LZ77 parse consists of $z$ phrases, with high probability we can build an LZ77-like parse of $S$ that consists of $\Oh{z / \epsilon}$ phrases using $\Oh{n^{1 + \epsilon}}$ time, $\Oh{n^{1 + \epsilon} / B}$ I/Os (where $B$ is the size of a disk block) and $\Oh{z / \epsilon}$ space.