Average linear time and compressed space construction of the burrows-wheeler transform

Abstract

The Burrows-Wheeler Transform is a text permutation that has revolutionized the fields of pattern matching and text compression, bridging the gap existing between the two. In this paper we approach the BWT-construction problem generalizing a well-known algorithm—based on backward search and dynamic strings manipulation—to work in a context-wise fashion, using automata on words. Let n, σ, and H k be the text length, the alphabet size, and the k-th order empirical entropy of the text, respectively. Moreover, let H ∗ k = min{H k +1, [log σ]}. Under the word RAM model with word size w ∈ Θ(log n), our algorithm builds theBWTin averageO(nH ∗ k) time using nH ∗ k +o(nH ∗ k) bits of space,where k = log σ (n/ log 2 n) − 1. We experimentally show that our algorithm has very good performances (essentially linear time) on DNA sequences, using about 2.6 bits per input symbol in RAM.