Space-efficient RLZ-to-LZ77 conversion

TL;DR

This paper presents a space-efficient method for converting RLZ to LZ77 parsing by leveraging a reference sequence and relative parsing, enabling fast construction with minimal space overhead.

Contribution

It introduces a novel algorithm that efficiently converts RLZ to LZ77 parsing using polylogarithmic time and linear space relative to the reference and parse size.

Findings

Conversion time is polylogarithmic in text length.

Space complexity is linear in reference and parse size.

Method improves efficiency over previous approaches.

Abstract

Consider a text $T [1..n]$ prefixed by a reference sequence $R = T [1..\ell]$. We show how, given $R$ and the $z'$-phrase relative Lempel-Ziv parse of $T [\ell + 1..n]$ with respect to $R$, we can build the LZ77 parse of $T$ in $n\,\mathrm{polylog} (n)$ time and $O (\ell + z')$ total space.