Lyndon Array Construction during Burrows-Wheeler Inversion

TL;DR

This paper introduces a linear-time algorithm for computing the Lyndon array during Burrows-Wheeler transform inversion, offering a space-efficient representation and competitive performance compared to existing methods.

Contribution

The paper presents a novel linear-time algorithm for Lyndon array construction integrated with Burrows-Wheeler inversion and a new space-efficient balanced parenthesis representation.

Findings

Algorithm runs in linear time using minimal extra space.

The approach is competitive with existing Lyndon array algorithms.

Proposes a space-efficient data structure supporting constant-time access.

Abstract

In this paper we present an algorithm to compute the Lyndon array of a string $T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler transform of $T$. Our algorithm runs in linear time using only a stack in addition to the data structures used for Burrows-Wheeler inversion. We compare our algorithm with two other linear-time algorithms for Lyndon array construction and show that computing the Burrows-Wheeler transform and then constructing the Lyndon array is competitive compared to the known approaches. We also propose a new balanced parenthesis representation for the Lyndon array that uses $2n+o(n)$ bits of space and supports constant time access. This representation can be built in linear time using $O(n)$ words of space, or in $O(n\log n/\log\log n)$ time using asymptotically the same space as $T$.