LZ-End Parsing in Compressed Space

TL;DR

This paper introduces an efficient algorithm for constructing the LZ-End parsing of strings, optimizing time and space, with practical streaming implementation and experimental validation against existing methods.

Contribution

It presents the first expected-time algorithm for LZ-End parsing with space efficiency and a streaming variant that is verified through experiments.

Findings

Algorithm operates in expected O(n log ℓ) time and O(z + ℓ) space.

Streaming implementation constructs parsing with one left-to-right pass and verification pass.

Experimental results show practical advantages over LZ77-based methods.

Abstract

We present an algorithm that constructs the LZ-End parsing (a variation of LZ77) of a given string of length $n$ in $O(n\log\ell)$ expected time and $O(z + \ell)$ space, where $z$ is the number of phrases in the parsing and $\ell$ is the length of the longest phrase. As an option, we can fix $\ell$ (e.g., to the size of RAM) thus obtaining a reasonable LZ-End approximation with the same functionality and the length of phrases restricted by $\ell$. This modified algorithm constructs the parsing in streaming fashion in one left to right pass on the input string w.h.p. and performs one right to left pass to verify the correctness of the result. Experimentally comparing this version to other LZ77-based analogs, we show that it is of practical interest.