A four-stage algorithm for updating a Burrows–Wheeler transform

We present a four-stage algorithm that updates the Burrows–Wheeler Transform of a text T, when this text is modified. The Burrows–Wheeler Transform is used by many text compression applications and some self-index data structures. It operates by reordering the letters of a text T to obtain a new text bwt(T) which can be better compressed.Even though recent advances are offering this structure new applications, a major bottleneck still exists: bwt(T) has to be entirely reconstructed from scratch whenever T is modified.We study how standard edit operations (insertion, deletion, substitution of a letter or a factor) that transform a text T into T′ impact bwt(T). Then we present an algorithm that directly converts bwt(T) into bwt(T′). Based on this algorithm, we also sketch a method for converting the suffix array of T into the suffix array of T′.We finally show, based on the experiments we conducted, that this algorithm, whose worst-case time complexity is O(|T|log|T|(1+logσ/loglog|T|)), performs really well in practice and replaces advantageously the traditional approach.