Left Lyndon tree construction

TL;DR

This paper introduces algorithms for constructing the left Lyndon tree and forest of a word, enabling efficient sorting of prefixes according to a specific infinite order, all in linear time.

Contribution

It extends Lyndon factorisation to tree structures and provides linear-time algorithms for their construction and prefix sorting.

Findings

Algorithms run in linear time on a general alphabet.

The methods enable efficient prefix sorting based on infinite order.

Extension from factorisation to tree and forest structures.

Abstract

We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al. (2019). A straightforward variant computes the left Lyndon forest of a word. All algorithms run in linear time on a general alphabet, that is, in the letter-comparison model.