Efficient Lyndon factorization of grammar compressed text

TL;DR

This paper introduces a polynomial-time algorithm for computing Lyndon factorization directly from grammar compressed text represented as an SLP, enabling efficient processing of exponentially large strings.

Contribution

The paper presents the first polynomial-time algorithm for Lyndon factorization of grammar compressed strings, improving efficiency over previous methods.

Findings

Algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space.

Enables Lyndon factorization of exponentially large strings from SLPs.

First polynomial-time solution for Lyndon factorization on grammar compressed text.

Abstract

We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the size of the Lyndon factorization, $n$ is the size of the SLP, and $h$ is the height of the derivation tree of the SLP. Since the length of the decompressed string can be exponentially large w.r.t. $n, m$ and $h$, our result is the first polynomial time solution when the string is given as SLP.