Burrows-Wheeler transform and LCP array construction in constant space

TL;DR

This paper presents an extension of an in-place BWT algorithm to compute the LCP array simultaneously in constant space, including a compressed representation, and explores time/space tradeoffs for indexing structure construction.

Contribution

It introduces a method to compute BWT and LCP arrays in constant space and in compressed form, advancing in-place algorithms for indexing structures.

Findings

Algorithm runs in quadratic time, similar to previous methods.

Supports computation of LCP array in compressed Elias coding.

Provides a time/space tradeoff analysis for in-place construction.

Abstract

In this article we extend the elegant in-place Burrows-Wheeler transform (BWT) algorithm proposed by Crochemore et al. (Crochemore et al., 2015). Our extension is twofold: we first show how to compute simultaneously the longest common prefix (LCP) array as well as the BWT, using constant additional space; we then show how to build the LCP array directly in compressed representation using Elias coding, still using constant additional space and with no asymptotic slowdown. Furthermore, we provide a time/space tradeoff for our algorithm when additional memory is allowed. Our algorithm runs in quadratic time, as does Crochemore et al.'s, and is supported by interesting properties of the BWT and of the LCP array, contributing to our understanding of the time/space tradeoff curve for building indexing structures.