In-Place BWT and Lyndon Array Construction in Constant Space

TL;DR

This paper introduces a novel in-place algorithm that constructs the Lyndon array during BWT computation using constant extra space, emphasizing conceptual simplicity over practical efficiency.

Contribution

It extends existing in-place BWT algorithms to also compute the Lyndon array with O(1) space, using a simple incremental approach.

Findings

Constructs Lyndon array in-place during BWT with constant space

Works for unbounded alphabets despite quadratic time complexity

Provides a conceptually simple method for Lyndon array computation

Abstract

We present an extension of the in-place BWT algorithm of Crochemore et al. [8] that enables the construction of the Lyndon array using O(1) extra space. Our approach incrementally maintains the lexicographic ranks of the suffixes during the right-to-left BWT construction and then derives the Lyndon array through a simple next-smaller-value procedure. Although not intended for practical use due to its quadratic running time, the method is conceptually simple and works for unbounded alphabets.