Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time

TL;DR

This paper presents a linear-time algorithm for constructing the bijective Burrows-Wheeler transform (BBWT), confirming a long-standing conjecture and improving previous non-linear time algorithms.

Contribution

It introduces a novel linear-time construction algorithm for the BBWT based on SAIS, matching the efficiency of the classical BWT construction.

Findings

BBWT can be constructed in linear time

The proposed algorithm improves previous results from super-linear to linear time

Confirms the conjecture that BBWT construction is feasible in linear time

Abstract

The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can also be constructed in linear time. We confirm this conjecture by proposing a construction algorithm that is based on SAIS, improving the best known result of $O(n \lg n /\lg \lg n)$ time to linear.