# Inducing the Lyndon Array

## TL;DR

This paper introduces a space-efficient linear-time algorithm for computing the Lyndon array and suffix array simultaneously, improving space requirements over previous methods and demonstrating practical speed and efficiency.

## Contribution

It presents a novel variant of induced suffix sorting that computes Lyndon and suffix arrays together in linear time using minimal space, surpassing prior algorithms.

## Key findings

- Uses $\sigma + O(1)$ words of space, reducing previous space requirements.
- Achieves linear time complexity for Lyndon array and suffix array computation.
- Experimental results show the algorithm is fast and space-efficient in practice.

## Abstract

In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $\sigma + O(1)$ words of working space, where $n$ is the length of the text and $\sigma$ is the alphabet size. Our result improves the previous best space requirement for linear time computation of the Lyndon array. In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use $O(n)$ words of working space in addition to the Lyndon array and suffix array. Experimental results with real and synthetic datasets show that our algorithm is not only space-efficient but also fast in practice.